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Publication:3446085
zbMath1123.65001MaRDI QIDQ3446085
Publication date: 13 June 2007
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
interpolationstabilityconvergenceGalerkin methodsplinestextbookmultivariate approximationerror boundsradial basis functionscollocationpositive definite functionsreproducing kernelskernel methodsmultiquadricsmeshless methodsspectral methodsmoving least-squaresthin-plate splinescattered data interpolationMatlab algorithms
Numerical computation using splines (65D07) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical interpolation (65D05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Spline approximation (41A15) Approximation by other special function classes (41A30)
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I: Theory. ⋮ On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space ⋮ Adaptive meshless centres and RBF stencils for Poisson equation ⋮ Numerical experiments on the condition number of the interpolation matrices for radial basis functions ⋮ CAD and mesh repair with radial basis functions ⋮ Scattered and track data interpolation using an efficient strip searching procedure ⋮ Quasi-interpolation for linear functional data ⋮ A fast object-oriented MATLAB implementation of the reproducing kernel particle method ⋮ The near-equivalence of five species of spectrally-accurate radial basis functions (RBFs): Asymptotic approximations to the RBF cardinal functions on a uniform, unbounded grid ⋮ Six strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite interval ⋮ Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via collocation method based on radial basis functions ⋮ Enhancing credit default swap valuation with meshfree methods ⋮ RBFs approximation method for time fractional partial differential equations ⋮ Gauss-Hermite quadratures for functions from Hilbert spaces with Gaussian reproducing kernels ⋮ The orthogonal gradients method: a radial basis functions method for solving partial differential equations on arbitrary surfaces ⋮ Multivariate Hermite-Birkhoff interpolation by a class of cardinal basis functions ⋮ A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains ⋮ Three-dimensional image reconstruction using the PF/MFS technique ⋮ A method for solving partial differential equations via radial basis functions: application to the heat equation ⋮ Numerical simulation of forward problem for electrical capacitance tomography using element-free Galerkin method ⋮ An integrated-RBF technique based on Galerkin formulation for elliptic differential equations ⋮ Numerical simulation of two-dimensional combustion using mesh-free methods ⋮ On the enriched RBF method for singular potential problems ⋮ Moving-boundary problems solved by adaptive radial basis functions ⋮ Three-dimensional modeling of heat transport in deep hydrothermal reservoirs ⋮ Accurate emulators for large-scale computer experiments ⋮ Spherical interpolation using the partition of unity method: an efficient and flexible algorithm ⋮ Multivariate interpolation with increasingly flat radial basis functions of finite smoothness ⋮ Reproducing kernels of generalized Sobolev spaces via a Green function approach with distributional operators ⋮ Wendland functions with increasing smoothness converge to a Gaussian ⋮ Bases for kernel-based spaces ⋮ Universal approximation by radial basis function networks of Delsarte translates ⋮ Regularized symmetric positive definite matrix factorizations for linear systems arising from RBF interpolation and differentiation ⋮ A comparison study of meshfree techniques for solving the two-dimensional linear hyperbolic telegraph equation ⋮ The numerical solution of Fokker-Planck equation with radial basis functions (RBFs) based on the meshless technique of Kansa's approach and Galerkin method ⋮ Numerical solution to time-dependent 4D inviscid Burgers' equations ⋮ Optimization, conditioning and accuracy of radial basis function method for partial differential equations with nonlocal boundary conditions -- a case of two-dimensional Poisson equation ⋮ An image denoising approach based on a meshfree method and the domain decomposition technique ⋮ Comparison of meshless local weak and strong forms based on particular solutions for a non-classical 2-D diffusion model ⋮ On the construction of nested space-filling designs ⋮ Convergence and error theorems for Hermite function pseudo-RBFs: interpolation on a finite interval by Gaussian-localized polynomials ⋮ Iterative dynamic analysis of linear and nonlinear fully saturated porous media considering edge-based smoothed meshfree techniques ⋮ Solving support vector machines in reproducing kernel Banach spaces with positive definite functions ⋮ Error-controlled global sensitivity analysis of ordinary differential equations ⋮ Optimal constant shape parameter for multiquadric based RBF-FD method ⋮ PetRBF - A parallel \(O(N)\) algorithm for radial basis function interpolation with Gaussians ⋮ On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation ⋮ A class of piecewise interpolating functions based on barycentric coordinates ⋮ Error estimate for the numerical solution of fractional reaction-subdiffusion process based on a meshless method ⋮ On the constrained mock-Chebyshev least-squares ⋮ Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme ⋮ Numerical solution of two-dimensional weakly singular stochastic integral equations on non-rectangular domains via radial basis functions ⋮ Some remarks on Trefftz type approximations ⋮ Quasi-interpolation operators on hexagonal grids with high approximation orders in spaces of polyharmonic splines ⋮ A radial basis function partition of unity collocation method for convection-diffusion equations arising in financial applications ⋮ Multiscale methods with compactly supported radial basis functions for the Stokes problem on bounded domains ⋮ On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs ⋮ Stable computations with flat radial basis functions using vector-valued rational approximations ⋮ Piece-wise moving least squares approximation ⋮ Radial basis functions method for valuing options: a multinomial tree approach ⋮ Positive constrained approximation via RBF-based partition of unity method ⋮ Optimal shape parameter for the solution of elastostatic problems with the RBF method ⋮ Trust-region methods for nonlinear elliptic equations with radial basis functions ⋮ A multigrid-like algorithm for probabilistic domain decomposition ⋮ A stochastic minimum principle and an adaptive pathwise algorithm for stochastic optimal control ⋮ A meshless method on non-Fickian flows with mixing length growth in porous media based on radial basis functions: a comparative study ⋮ A scheme for interpolation by Hankel translates of a basis function ⋮ On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions ⋮ Surrogate-enhanced simulation of aircraft in trimmed state ⋮ Spectral collocation and radial basis function methods for one-dimensional interface problems ⋮ Compact local integrated-RBF approximations for second-order elliptic differential problems ⋮ High accuracy multiquadric quasi-interpolation ⋮ Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions ⋮ Dynamic programming using radial basis functions ⋮ Adaptive scattered data fitting by extension of local approximations to hierarchical splines ⋮ Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions ⋮ A new meshless approach for three dimensional fluid flow and related heat transfer problems ⋮ Enhancing finite differences with radial basis functions: experiments on the Navier-Stokes equations ⋮ The role of inner summaries in the fast evaluation of thin-plate splines ⋮ Lobachevsky spline functions and interpolation to scattered data ⋮ Uncertainty quantification in bending analysis of moderately thick plates with elastically restrained edges using the Chaotic Radial Basis function ⋮ The numerical solution of nonlinear high dimensional generalized Benjamin-Bona-Mahony-Burgers equation via the meshless method of radial basis functions ⋮ A meshless RBF method for computing a numerical solution of unsteady Burgers'-type equations ⋮ Partition of unity interpolation using stable kernel-based techniques ⋮ On the role of polynomials in RBF-FD approximations. III: Behavior near domain boundaries ⋮ A RBF-based differential quadrature method for solving two-dimensional variable-order time fractional advection-diffusion equation ⋮ Meshless technique for the solution of time-fractional partial differential equations having real-world applications ⋮ Managing geological uncertainty in expensive reservoir simulation optimization ⋮ A mesh-free pseudospectral approach to estimating the fractional Laplacian via radial basis functions ⋮ Novel multilevel techniques for convergence acceleration in the solution of systems of equations arising from RBF-FD meshless discretizations ⋮ Kernel-based collocation methods for heat transport on evolving surfaces ⋮ A novel class of stabilized greedy kernel approximation algorithms: convergence, stability and uniform point distribution ⋮ Numerical simulation of a prostate tumor growth model by the RBF-FD scheme and a semi-implicit time discretization ⋮ A stable RBF partition of unity local method for elliptic interface problems in two dimensions ⋮ RBF-FD solution for a financial partial-integro differential equation utilizing the generalized multiquadric function ⋮ Convergence of some mean field games systems to aggregation and flocking models ⋮ Recovering functions: a method based on domain decomposition ⋮ Local interpolation schemes for landmark-based image registration: a comparison ⋮ The extension of Rippa's algorithm beyond LOOCV ⋮ Linking physics and spatial statistics: a new family of Boltzmann-Gibbs random fields ⋮ Mesh-free error integration in arbitrary dimensions: a numerical study of discrepancy functions ⋮ Closed form representations and properties of the generalised Wendland functions ⋮ Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model ⋮ A rational RBF interpolation with conditionally positive definite kernels ⋮ A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics ⋮ Micro-combustion modelling with RBF-FD: a high-order meshfree method for reactive flows in complex geometries ⋮ Hybrid radial basis function methods of lines for the numerical solution of viscous Burgers' equation ⋮ RBF moment computation and meshless cubature on general polygonal regions ⋮ A time-efficient variable shape parameter Kansa-radial basis function method for the solution of nonlinear boundary value problems ⋮ Phase distribution control of neural oscillator populations using local radial basis function meshfree technique with application in epileptic seizures: a numerical simulation approach ⋮ A strong-form local meshless approach based on radial basis function-finite difference (RBF-FD) method for solving multi-dimensional coupled damped Schrödinger system appearing in Bose-Einstein condensates ⋮ Implicit reconstructions of thin leaf surfaces from large, noisy point clouds ⋮ Perturbation of the eigenvectors of the graph Laplacian: application to image denoising ⋮ Inverting nonlinear dimensionality reduction with scale-free radial basis function interpolation ⋮ An introduction to the Hilbert-Schmidt SVD using iterated Brownian bridge kernels ⋮ An SVD analysis of equispaced polynomial interpolation ⋮ Meshless methods for solving Dirichlet boundary optimal control problems governed by elliptic PDEs ⋮ Fast and exact synthesis of some operator scaling Gaussian random fields ⋮ Error indicators and refinement strategies for solving Poisson problems through a RBF partition of unity collocation scheme ⋮ Testing the accomplishment of the radial integration method with the direct interpolation boundary element technique for solving Helmholtz problems ⋮ Implicit surface reconstruction with radial basis functions via PDEs ⋮ Hermite type radial basis function-based differential quadrature method for higher order equations ⋮ Weighted proper orthogonal decomposition of the swirling flow exiting the hydraulic turbine runner ⋮ Optimal Hölder-Zygmund exponent of semi-regular refinable functions ⋮ Explicit time stepping of PDEs with local refinement in space-time ⋮ Fast high-dimensional node generation with variable density ⋮ On a generalized Gaussian radial basis function: analysis and applications ⋮ Radial basis function approximations: comparison and applications ⋮ Strong-form approach to elasticity: hybrid finite difference-meshless collocation method (FDMCM) ⋮ An element-free Galerkin meshless method for simulating the behavior of cancer cell invasion of surrounding tissue ⋮ A local radial basis function collocation method for band structure computation of phononic crystals with scatterers of arbitrary geometry ⋮ A meshfree numerical technique based on radial basis function pseudospectral method for Fisher's equation ⋮ Numerical investigation of the nonlinear modified anomalous diffusion process ⋮ A modified moving least-squares suitable for scattered data fitting with outliers ⋮ An algorithm for solving a class of multiplayer feedback-Nash differential games ⋮ Direct and integrated radial functions based quasilinearization schemes for nonlinear fractional differential equations ⋮ Numerical solutions of time-fractional coupled viscous Burgers' equations using meshfree spectral method ⋮ A stable meshfree PDE solver for source-type flows in porous media ⋮ An efficient trivariate algorithm for tetrahedral Shepard interpolation ⋮ On the positivity and magnitudes of Bayesian quadrature weights ⋮ A block positive-semidefinite splitting preconditioner for generalized saddle point linear systems ⋮ A flux-corrected RBF-FD method for convection dominated problems in domains and on manifolds ⋮ Implicit surface reconstruction based on generalized radial basis functions interpolant with distinct constraints ⋮ A boundary integral method for modelling vibroacoustic energy distributions in uncertain built up structures ⋮ RBF-LOI: augmenting radial basis functions (RBFs) with least orthogonal interpolation (LOI) for solving PDEs on surfaces ⋮ Kernel-based probability measures for generalized interpolations: a deterministic or stochastic problem? ⋮ The meshless Kansa method for time-fractional higher order partial differential equations with constant and variable coefficients ⋮ Radial discrete PDE splines on Lipschitz domains ⋮ Modified numerical approaches for a class of Volterra integral equations with proportional delays ⋮ The role of Hilbert-Schmidt SVD basis in Hermite-Birkhoff interpolation in fractional sense ⋮ Sparse radial basis function approximation with spatially variable shape parameters ⋮ Variable shape parameter Kansa RBF method for the solution of nonlinear boundary value problems ⋮ Application of meshfree spectral method for the solution of multi-dimensional time-fractional Sobolev equations ⋮ Free and forced vibration analysis of moderately thick plates with uncertain material properties using the Chaotic Radial Basis Function ⋮ Two-dimensional simulation of the damped Kuramoto-Sivashinsky equation via radial basis function-generated finite difference scheme combined with an exponential time discretization ⋮ An efficient method based on RBFs for multilayer data interpolation with application in air pollution data analysis ⋮ Numerical analysis of time fractional Black-Scholes European option pricing model arising in financial market ⋮ An improved hybrid-ORBIT algorithm based on point sorting and MLE technique ⋮ A kernel-based technique to solve three-dimensional linear Fredholm integral equations of the second kind over general domains ⋮ Solving elliptic PDE's on domains with curved boundaries with an immersed penalized boundary method ⋮ Comparison of moving least squares and RBF+poly for interpolation and derivative approximation ⋮ Numerical solution of two-dimensional nonlinear sine-Gordon equation using localized method of approximate particular solutions ⋮ Numerical investigation of ferrofluid convection with Kelvin forces and non-Darcy effects ⋮ Selection of shape parameter in radial basis functions for solution of time-fractional Black-Scholes models ⋮ Numerical simulations of nonlocal phase-field and hyperbolic nonlocal phase-field models via localized radial basis functions-based pseudo-spectral method (LRBF-PSM) ⋮ Symmetric radial basis function method for simulation of elliptic partial differential equations ⋮ Approximation in weighted \(p\)-mean by RBF networks of Delsarte translates ⋮ Numerical Caputo differentiation by radial basis functions ⋮ A numerical algorithm for multidimensional modeling of scattered data points ⋮ A computational tool for comparing all linear PDE solvers ⋮ Wiener's tauberian theorems for the Fourier-Bessel transformation and uniform approximation by RBF networks of Delsarte translates ⋮ A radial basis function (RBF)-finite difference (FD) method for diffusion and reaction-diffusion equations on surfaces ⋮ Convexity and solvability for compactly supported radial basis functions with different shapes ⋮ Error analysis of method of lines (MOL) via generalized interpolating moving least squares (GIMLS) approximation ⋮ Concentration inequalities for cross-validation in scattered data approximation ⋮ Anti-aliasing of gray-scale/color/outline images: looking through the lens of numerical approaches for PDE-based models ⋮ Efficient image denoising technique using the meshless method: investigation of operator splitting RBF collocation method for two anisotropic diffusion-based PDEs ⋮ Transport schemes in spherical geometries using spline-based RBF-FD with polynomials ⋮ Analysis of geometric uncertainties in CFD problems solved by RBF-FD meshless method ⋮ Radial basis functions based meshfree schemes for the simulation of non-linear extended Fisher-Kolmogorov model ⋮ Optimal design for kernel interpolation: applications to uncertainty quantification ⋮ Simple and reliable boundary detection for meshfree particle methods using interval analysis ⋮ A polynomial-augmented RBF collocation method using fictitious centres for solving the Cahn-Hilliard equation ⋮ An efficient local RBF-based method for elasticity problems involving multiple material phases ⋮ RBF approximation of three dimensional PDEs using tensor Krylov subspace methods ⋮ Numerical evaluation of the fractional Klein-Kramers model arising in molecular dynamics ⋮ A greedy non-intrusive reduced order model for shallow water equations ⋮ Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study ⋮ An efficient high-order meshless method for advection-diffusion equations on time-varying irregular domains ⋮ Meshless symplectic and multi-symplectic local RBF collocation methods for nonlinear Schrödinger equation ⋮ Gaussian radial basis function and quadrature sinc method for two-dimensional space-fractional diffusion equations ⋮ An approach to adaptive refinement for the RBF-FD method for 2D elliptic equations ⋮ Effective condition number for the selection of the RBF shape parameter with the fictitious point method ⋮ A stochastic extended Rippa's algorithm for LpOCV ⋮ Efficient reduced basis algorithm (ERBA) for kernel-based approximation ⋮ RBF WENO reconstructions with adaptive order and applications to conservation laws ⋮ A meshless multi-symplectic local radial basis function collocation scheme for the ``good Boussinesq equation ⋮ Embedded domain reduced basis models for the shallow water hyperbolic equations with the shifted boundary method ⋮ A direct RBF-PU method for simulating the infiltration of cytotoxic T-lymphocytes into the tumor microenvironment ⋮ Refined error estimates for Green kernel-based interpolation ⋮ Coupled Kansa and hybrid optimization methodological approach for Kolmogorov-Feller equations ⋮ Development of a WENO scheme based on radial basis function with an improved convergence order ⋮ A local scheme for numerical simulation of multi-dimensional dynamic quantum model: application to decision-making ⋮ Application of Hilbert-Schmidt SVD approach to solve linear two-dimensional Fredholm integral equations of the second kind ⋮ Octant-based stencil selection for meshless finite difference methods in 3D ⋮ Sixth-order accurate schemes for reinitialization and extrapolation in the level set framework ⋮ A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation ⋮ European option valuation under the Bates PIDE in finance: a numerical implementation of the Gaussian scheme ⋮ An adaptive LOOCV-based refinement scheme for RBF collocation methods over irregular domains ⋮ Pseudospectral meshless radial point interpolation for generalized biharmonic equation in the presence of Cahn-Hilliard conditions ⋮ Adaptive procedures for meshfree RBF unsymmetric and symmetric collocation methods ⋮ Jumping with variably scaled discontinuous kernels (VSDKs) ⋮ RBF methods in a stochastic volatility framework for Greeks computation ⋮ Generation of point sets by convex optimization for interpolation in reproducing kernel Hilbert spaces ⋮ Completion of right-hand side in the frame of inverse Cauchy problem of elliptic type equation through homogenization meshless collocation method ⋮ A two-stage adaptive scheme based on RBF collocation for solving elliptic PDEs ⋮ An iterated quasi-interpolation approach for derivative approximation ⋮ Error analysis of the reduced RBF model based on POD method for time-fractional partial differential equations ⋮ An integral equation-based numerical method for the forced heat equation on complex domains ⋮ Multiscale radial kernels with high-order generalized Strang-Fix conditions ⋮ A symplectic procedure for two-dimensional coupled elastic wave equations using radial basis functions interpolation ⋮ An insight into RBF-FD approximations augmented with polynomials ⋮ A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels ⋮ Mesh free alternate directional implicit method based three dimensional super-diffusive model for benign brain tumor segmentation ⋮ On the pricing of multi-asset options under jump-diffusion processes using meshfree moving least-squares approximation ⋮ On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models ⋮ Inverse multi-quadric RBF for computing the weights of FD method: application to American options ⋮ Kansa radial basis function method with fictitious centres for solving nonlinear boundary value problems ⋮ Numerical investigation of fractional nonlinear sine-Gordon and Klein-Gordon models arising in relativistic quantum mechanics ⋮ An adaptive sparse kernel technique in greedy algorithm framework to simulate an anomalous solute transport model ⋮ Simulating backward wave propagation in metamaterial with radial basis functions ⋮ Improved numerical solution of multi-asset option pricing problem: a localized RBF-FD approach ⋮ MHD natural convection in a cavity in the presence of cross partial magnetic fields and Al\(_2\)O\(_3\)-water nanofluid ⋮ Coupling of the Crank-Nicolson scheme and localized meshless technique for viscoelastic wave model in fluid flow ⋮ Learning via variably scaled kernels ⋮ Solving Poisson equation with Dirichlet conditions through multinode Shepard operators ⋮ Numerical simulation of fractional evolution model arising in viscoelastic mechanics ⋮ Partition of unity methods for signal processing on graphs ⋮ Meshless symplectic and multi-symplectic local RBF collocation methods for Hamiltonian PDEs ⋮ Effects of partial magnetic field in a vented square cavity with aiding and opposing of MWCNT-water nanofluid flows ⋮ The fragile points method (FPM) to solve two-dimensional hyperbolic telegraph equation using point stiffness matrices ⋮ Construction of new cubic Bézier-like triangular patches with application in scattered data interpolation ⋮ Convergence rate estimates for the kernelized predictor corrector method for fractional order initial value problems ⋮ An efficient PODI method for real-time simulation of indenter contact problems using RBF interpolation and contact domain decomposition ⋮ RBFCUB: a numerical package for near-optimal meshless cubature on general polygons ⋮ A discrete collocation scheme to solve Fredholm integral equations of the second kind in high dimensions using radial kernels ⋮ On efficient design of pilot experiment for generalized linear models ⋮ An overlapping domain decomposition Schwarz method applied to the method of fundamental solution ⋮ Application of combination schemes based on radial basis functions and finite difference to solve stochastic coupled nonlinear time fractional sine-Gordon equations ⋮ Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks ⋮ A forward-backward greedy approach for sparse multiscale learning ⋮ Numerical study of high order nonlinear dispersive PDEs using different RBF approaches ⋮ A localized meshless technique for solving 2D nonlinear integro-differential equation with multi-term kernels ⋮ Soliton wave solutions of nonlinear mathematical models in elastic rods and bistable surfaces ⋮ Meshless symplectic and multi-symplectic algorithm for Klein-Gordon-Schrödinger system with local RBF collocation ⋮ A POD-RBF-FD scheme for simulating chemotaxis models on surfaces ⋮ Residual-error cross-validation method for selecting a suitable shape parameter for RBF interpolation ⋮ An efficient operator-splitting radial basis function-generated finite difference (RBF-FD) scheme for image noise removal based on nonlinear total variation models ⋮ Samplets: construction and scattered data compression ⋮ Coupling RBF-based meshless method and Landweber iteration algorithm for approximating a space-dependent source term in a time fractional diffusion equation ⋮ An adaptive residual sub-sampling algorithm for kernel interpolation based on maximum likelihood estimations ⋮ Acceleration of RBF-FD meshless phase-field modelling of dendritic solidification by space-time adaptive approach ⋮ Training RBF neural networks for the solution of elliptic boundary value problems ⋮ Fast meshfree methods for nonlinear radiation diffusion equation ⋮ Solitary wave propagation of the generalized Kuramoto-Sivashinsky equation in fragmented porous media ⋮ An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing ⋮ An interpolating particle method for the Vlasov-Poisson equation ⋮ Localized meshless approaches based on theta method and BDF2 for nonlinear Sobolev equation arising from fluid dynamics ⋮ Rectangular eigenvalue problems ⋮ An asymptotic analysis and numerical simulation of a prostate tumor growth model via the generalized moving least squares approximation combined with semi-implicit time integration ⋮ Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks ⋮ A time-splitting local meshfree approach for time-fractional anisotropic diffusion equation: application in image denoising ⋮ Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces ⋮ Simulation of electromagnetic wave propagations in negative index materials by the localized RBF-collocation method ⋮ Comparative analysis of machine learning methods for active flow control ⋮ A de-singularized meshfree approach to default probability estimation under a regime-switching synchronous-jump tempered stable Lévy model ⋮ Quantum radial basis function method for the Poisson equation ⋮ Meshfree methods for two-dimensional three-temperature radiation diffusion equations ⋮ A meshless multiscale method for simulating hemodynamics ⋮ Study of the fragile points method for solving two-dimensional linear and nonlinear wave equations on complex and cracked domains ⋮ Solving Nonlinear Elliptic PDEs in 2D and 3D Using Polyharmonic Splines and Low-Degree of Polynomials ⋮ \(\ell_1\)-constrained implied transition densities ⋮ Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives ⋮ Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient ⋮ Stochastic collocation for optimal control problems with stochastic PDE constraints by meshless techniques ⋮ A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary conditions ⋮ An outlier detection and recovery method based on moving least squares quasi-interpolation scheme and \(\text{ł}_0\)-minimization problem ⋮ A modified RBF collocation method for solving the convection-diffusion problems ⋮ The smooth extension embedding method with Chebyshev polynomials ⋮ Error estimates of divergence-free generalized moving least squares (div-free GMLS) derivatives approximations in Sobolev spaces ⋮ Covariance models and Gaussian process regression for the wave equation. Application to related inverse problems ⋮ A hybrid radial basis functions collocation technique to numerically solve fractional advection–diffusion models ⋮ Optimal uniform error estimates for moving <scp>least‐squares</scp> collocation with application to option pricing under jump‐diffusion processes ⋮ On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation ⋮ Quasi-uniform designs with optimal and near-optimal uniformity constant ⋮ On optimal radius of sub-domains in meshless LBIE method ⋮ Multi-dimensional summation-by-parts operators for general function spaces: theory and construction ⋮ A 2D prediction step using multiquadric local interpolation with adaptive parameter estimation for image compression ⋮ A New Certified Hierarchical and Adaptive RB-ML-ROM Surrogate Model for Parametrized PDEs ⋮ Approximate solution of two dimensional linear and nonlinear stochastic Itô-Volterra integral equations via meshless scheme ⋮ On the fractional Laplacian of some positive definite kernels with applications in numerically solving the surface quasi-geostrophic equation as a prominent fractional calculus model ⋮ Meshfree methods for the variable-order fractional advection-diffusion equation ⋮ High order multiquadric trigonometric quasi-interpolation method for solving time-dependent partial differential equations ⋮ A fault detection method based on partition of unity and kernel approximation ⋮ HJB-RBF based approach for the control of PDEs ⋮ Unnamed Item ⋮ Solving 2D damped Kuramoto-Sivashinsky with multiple relaxation time lattice Boltzmann method ⋮ High-dimensional approximation with kernel-based multilevel methods on sparse grids ⋮ CURVATURE BASED CHARACTERIZATION OF RADIAL BASIS FUNCTIONS: APPLICATION TO INTERPOLATION ⋮ A meshless Runge-Kutta method for some nonlinear PDEs arising in physics ⋮ An efficient localized meshless collocation method for the two-dimensional Burgers-type equation arising in fluid turbulent flows ⋮ Meshfree methods for nonlinear equilibrium radiation diffusion equation ⋮ Radial basis function partition of unity procedure combined with the reduced-order method for solving Zakharov-Rubenchik equations ⋮ Solution of time‐fractional stochastic nonlinear sine‐Gordon equation via finite difference and meshfree techniques ⋮ An RBF-FD method for numerical solutions of 2D diffusion-wave and diffusion equations of distributed fractional order ⋮ Bayesian approach for radial kernel parameter tuning ⋮ Adaptive residual Refinement in an RBF Finite difference scheme for 2D time-dependent problems ⋮ Data-Driven Kernel Designs for Optimized Greedy Schemes: A Machine Learning Perspective ⋮ Improved stencil selection for meshless finite difference methods in 3D ⋮ Error and stability estimates of a time-fractional option pricing model under fully spatial-temporal graded meshes ⋮ Numerical approximation of the first-passage time distribution of time-varying diffusion decision models: a mesh-free approach ⋮ An RBF-FD method for the time-fractional advection-dispersion equation with nonlinear source term ⋮ Simulations of dendritic solidification via the diffuse approximate method ⋮ A multiscale RBF method for severely ill-posed problems on spheres ⋮ A variable projection method for the general radial basis function neural network ⋮ The space-time kernel-based numerical method for Burgers' equations ⋮ A new variable shape parameter strategy for RBF approximation using neural networks ⋮ Reproducing kernels of Sobolev–Slobodeckij˘ spaces via Green’s kernel approach: Theory and applications ⋮ \texttt{GLISp-r}: a preference-based optimization algorithm with convergence guarantees ⋮ Moving least squares approximation using variably scaled discontinuous weight function ⋮ A Fully Implicit Method Using Nodal Radial Basis Functions to Solve the Linear Advection Equation ⋮ Error bounds for a least squares meshless finite difference method on closed manifolds ⋮ Random sampling and unisolvent interpolation by almost everywhere analytic functions ⋮ An RBF-PUM finite difference scheme for forward-backward heat equation ⋮ The enhanced boundary knot method with fictitious sources for solving Helmholtz-type equations ⋮ Energy-stable global radial basis function methods on summation-by-parts form ⋮ Hybrid high-resolution RBF-ENO method ⋮ A finite difference/Kansa method for the two-dimensional time and space fractional Bloch-Torrey equation ⋮ Utilizing differential quadrature-based RBF partition of unity collocation method to simulate distributed-order time fractional cable equation ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Complete Hermite-Birkhoff interpolation on scattered data by combined Shepard operators ⋮ Sparse Inpainting with Smoothed Particle Hydrodynamics ⋮ VOLATILITY SMILE INTERPOLATION WITH RADIAL BASIS FUNCTIONS ⋮ Numerical simulation for a time-fractional coupled nonlinear Schrödinger equations ⋮ Approximation of insurance liability contracts using radial basis functions ⋮ A priori error estimates of a meshless method for optimal control problems of stochastic elliptic PDEs ⋮ Numerical solutions of strongly non-linear generalized Burgers–Fisher equation via meshfree spectral technique ⋮ A local meshless procedure to determine the unknown control parameter in the multi-dimensional inverse problems ⋮ Implicit Surface Reconstruction With a Curl-Free Radial Basis Function Partition of Unity Method ⋮ An Efficient Numerical Scheme for the Solution of a Stochastic Volatility Model Including Contemporaneous Jumps in Finance ⋮ An RBF approach for oil futures pricing under the jump-diffusion model ⋮ Numerical simulation of the biosensors in a trigger mode based on Michaelis-Menten enzymatic reaction ⋮ Generalizations of Simple Kriging Methods in Spatial Data Analysis ⋮ Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs ⋮ Kernel-Based Discretization for Solving Matrix-Valued PDEs ⋮ RBF methods for solving laterally averaged Saint Venant equations: application to eutrophication prevention through aeration ⋮ Stable Likelihood Computation for Gaussian Random Fields ⋮ Graphical Representation of Separatrices of Attraction Basins in Two and Three-Dimensional Dynamical Systems ⋮ An Efficient Local RBF Meshless Scheme for Steady Convection–Diffusion Problems ⋮ Padua points and fake nodes for polynomial approximation: old, new and open problems ⋮ Unnamed Item ⋮ A homotopy method for multikernel-based approximation ⋮ Unnamed Item ⋮ Robust Node Generation for Mesh-free Discretizations on Irregular Domains and Surfaces ⋮ Solving PDEs with a Hybrid Radial Basis Function: Power-Generalized Multiquadric Kernel ⋮ A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models ⋮ Numerical solution of the Allen-Cahn equation by using ”shifted” surface spline radial basis functions ⋮ A Kernel-Based Meshless Conservative Galerkin Method for Solving Hamiltonian Wave Equations ⋮ On fast computation of finite-time coherent sets using radial basis functions ⋮ A Least Squares Radial Basis Function Partition of Unity Method for Solving PDEs ⋮ Adaptive Meshfree Backward SDE Filter ⋮ A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces ⋮ A Kernel-Based Embedding Method and Convergence Analysis for Surfaces PDEs ⋮ Hierarchical Matrix Approximation for Kernel-Based Scattered Data Interpolation ⋮ Asymptotic and Numerical Analysis of a Stochastic PDE Model of Volume Transmission ⋮ $H^2$-Convergence of Least-Squares Kernel Collocation Methods ⋮ A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli ⋮ A Rescaled Method for RBF Approximation ⋮ Kernel-Based Approximation Methods for Partial Differential Equations: Deterministic or Stochastic Problems? ⋮ Solving Partial Differential Equations with Multiscale Radial Basis Functions ⋮ On meshfree numerical differentiation ⋮ NEW MODEL FOR PRICING QUANTO CREDIT DEFAULT SWAPS ⋮ A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds ⋮ Generalized Mercer Kernels and Reproducing Kernel Banach Spaces ⋮ Isotropic positive definite functions on spheres generated from those in Euclidean spaces ⋮ A Domain Decomposition Multilevel Preconditioner for Interpolation with Radial Basis Functions ⋮ An Adaptive LOOCV-Based Algorithm for Solving Elliptic PDEs via RBF Collocation ⋮ Penalty-free method for nonsmooth constrained optimization via radial basis functions ⋮ Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method ⋮ Nonlinear system identification using radial basis functions ⋮ Spectral Properties of Kernel Matrices in the Flat Limit ⋮ A meshless Galerkin method for non-local diffusion using localized kernel bases ⋮ Hybrid shape parameter strategy for the RBF approximation of vibrating systems ⋮ On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method ⋮ Solving Fourth-Order PDEs using the LMAPS ⋮ LOCALIZED RADIAL BASIS FUNCTIONS FOR NO-ARBITRAGE PRICING OF OPTIONS UNDER STOCHASTIC ALPHA–BETA–RHO DYNAMICS ⋮ Spectral analysis and preconditioning techniques for radial basis function collocation matrices ⋮ Radial positive definite functions and spectral theory of the Schrödinger operators with point interactions ⋮ Local RBF Algorithms for Elliptic Boundary Value Problems in Annular Domains ⋮ A high-order approximation method for semilinear parabolic equations on spheres ⋮ Collocation Methods for Cauchy Problems of Elliptic Operators via Conditional Stabilities ⋮ Lévy Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences ⋮ Improved RBF Collocation Methods for Fourth Order Boundary Value Problems ⋮ Cholesky-Based Experimental Design for Gaussian Process and Kernel-Based Emulation and Calibration ⋮ On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation ⋮ Numerical integration on multivariate scattered data by Lobachevsky splines ⋮ Positivity of Integrals for Higher Order $\nabla-$Convex and Completely Monotonic Functions ⋮ An iterative meshfree method for the elliptic monge–ampère equation in 2D ⋮ Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space ⋮ Stability of Energy Transfer in the Weak Coupling Method ⋮ A Meshless Technique Based on Integrated Radial Basis Function Networks for Elliptic Partial Differential Equations ⋮ Unnamed Item ⋮ Robust FEM-Based Extraction of Finite-Time Coherent Sets Using Scattered, Sparse, and Incomplete Trajectories ⋮ An RBF-Pseudospectral Approach for the Static and Vibration Analysis of Composite Plates Using a Higher-Order Theory ⋮ Preconditioning of Radial Basis Function Interpolation Systems via Accelerated Iterated Approximate Moving Least Squares Approximation ⋮ Feature augmentation for the inversion of the Fourier transform with limited data ⋮ A Local Radial Basis Function Method for High-Dimensional American Option Pricing Problems ⋮ Domain-type RBF Collocation Methods for Biharmonic Problems ⋮ Sequential Stochastic Response Surface Method Using Moving Least Squares-Based Sparse Grid Scheme for Efficient Reliability Analysis ⋮ Greedy Kernel Approximation for Sparse Surrogate Modeling ⋮ Node adaptive domain decomposition method by radial basis functions ⋮ Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Applications to Contour Lines, Sparse Data, and Inpainting ⋮ Pseudospectral Meshless Radial Point Hermit Interpolation Versus Pseudospectral Meshless Radial Point Interpolation ⋮ Solving fractional diffusion equations by Sinc and radial basis functions ⋮ A Unified Meshfree Pseudospectral Method for Solving Both Classical and Fractional PDEs ⋮ Space-time meshfree collocation method: Methodology and application to initial-boundary value problems ⋮ Radial basis function neural networks of Hankel translates as universal approximators ⋮ A meshless computational approach for solving two-dimensional inverse time-fractional diffusion problem with non-local boundary condition ⋮ A Partition of Unity Method for Divergence-Free or Curl-Free Radial Basis Function Approximation ⋮ A Trivariate Interpolation Algorithm Using a Cube-Partition Searching Procedure ⋮ $C^\infty$ Compactly Supported and Positive Definite Radial Kernels ⋮ A Meshfree Method for a PDE-Constrained Optimization Problem ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Multiscale Approximation and Reproducing Kernel Hilbert Space Methods ⋮ The Direct Radial Basis Function Partition of Unity (D-RBF-PU) Method for Solving PDEs ⋮ Multilevel RBF collocation method for the fourth-order thin plate problem ⋮ The Smooth Extension Embedding Method ⋮ The Method of Fundamental Solutions in Solving Coupled Boundary Value Problems for M/EEG ⋮ Radial-basis-function-based finite difference operator splitting method for pricing American options ⋮ Numerical treatment of nonlinear Volterra integral equations of Urysohn type with proportional delay ⋮ A Novel Surface Remeshing Scheme via Radial Basis Functions and Higher-Dimensional Embedding ⋮ An efficient method for mixed integral equations with phase lag
Uses Software
