A method for numerical integration on an automatic computer
From MaRDI portal
Publication:772331
DOI10.1007/BF01386223zbMath0093.14006OpenAlexW1971099220MaRDI QIDQ772331
Publication date: 1960
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/131456
Related Items
BDF-type shifted Chebyshev approximation scheme for fractional functional differential equations with delay and its error analysis, Averaged Gauss quadrature formulas: properties and applications, Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations, Volterra method for the radial Schrödinger equation, Extensions of Clenshaw-Curtis-type rules to integrals over a semi-infinite interval, Stable high-order cubature formulas for experimental data, Numerical experiments on the accuracy of the Chebyshev-Frobenius companion matrix method for finding the zeros of a truncated series of Chebyshev polynomials, A new robust line search technique based on Chebyshev polynomials, Fast, numerically stable computation of oscillatory integrals with stationary points, Generalized Clenshaw-Curtis quadrature rule with application to a collocation least-squares method, Fredholm integral equation method for the integro-differential Schrödinger equation, Singular value decomposition solution of the Schrödinger equation in the presence of exchange terms, A fast realization of preconditioned conjugate gradients for Wiener-Hopf integral equations, Evaluation of counterparty risk for derivatives with early-exercise features, Quadrature methods based on the Clenshaw-Curtis method of integration, Filon-Clenshaw-Curtis formulas for highly oscillatory integrals in the presence of stationary points, Sparse pseudo spectral projection methods with directional adaptation for uncertainty quantification, Numerical solutions of fractional optimal control with Caputo-Katugampola derivative, On quadrature of highly oscillatory integrals with logarithmic singularities, Sparse grid method for highly efficient computation of exposures for xVA, Uniform approximation to Cauchy principal value integrals with logarithmic singularity, A hybrid numerical method for solving system of high order boundary value problems, Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability, A simple, efficient and more reliable scheme for automatic numerical integration, A hybrid approximation scheme for discretizing constrained quadratic optimal control problems, Spectral solutions for differential and integral equations with varying coefficients using classical orthogonal polynomials, Pseudospectral methods for density functional theory in bounded and unbounded domains, Chebfun and numerical quadrature, A directional approach to gradual cover, Numerical method for a Markov-modulated risk model with two-sided jumps, Error transport equation boundary conditions for the Euler and Navier-Stokes equations, A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media, A new method for reconstruction of cross-sections using Tucker decomposition, On a certain adaptive method of approximate integration and its stopping criterion, Asymptotic expansions and fast computation of oscillatory Hilbert transforms, A new semi-analytical method with diagonal coefficient matrices for potential problems, Analysis of elastostatic problems using a semi-analytical method with diagonal coefficient matrices, A short tale of long tail integration, Efficient order-adaptive methods for polymer self-consistent field theory, A sinc quadrature subroutine for Cauchy principal value integrals, A comparison of some methods for the evaluation of highly oscillatory integrals, A truncated Clenshaw-Curtis formula approximates integrals over a semi-infinite interval, On fast and stable implementation of Clenshaw-Curtis and Fejér-type quadrature rules, Clenshaw-Curtis algorithms for an efficient numerical approximation of singular and highly oscillatory Fourier transform integrals, Fast computation of singular oscillatory Fourier transforms, Constructive polynomial approximation on the sphere, Estimating the error in matrix function approximations, Computational methods for solving the steady flow of a third grade fluid in a porous half space, Anti-Gaussian quadrature formulae based on the zeros of Stieltjes polynomials, A numerical method for solving shortest path problems, Optimization via Chebyshev polynomials, Orthogonal collocation revisited, Modified anti-Gauss and degree optimal average formulas for Gegenbauer measure, A compressed-sensing approach for closed-loop optimal control of nonlinear systems, On evaluation of Bessel transforms with oscillatory and algebraic singular integrands, On fast multipole methods for Volterra integral equations with highly oscillatory kernels, Uniform approximation to finite Hilbert transform of oscillatory functions and its algorithm, Superconvergence of a Chebyshev spectral collocation method, On convergence rates of Fejér and Gauss-Chebyshev quadrature rules, Explicit cost bounds of stochastic Galerkin approximations for parameterized PDEs with random coefficients, A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions, Clenshaw-Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels, Fractional pseudospectral integration/differentiation matrix and fractional differential equations, Gauss rules associated with nearly singular weights, Shifted GMRES for oscillatory integrals, Adaptive bivariate Chebyshev approximation, Fast memory efficient evaluation of spherical polynomials at scattered points, A quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight-function, Volterra type integral equation method for the radial Schrödinger equation: Single channel case, A numerical method for the expected penalty-reward function in a Markov-modulated jump-diffusion process, Chebyshev series expansion of inverse polynomials, Rarefied gas flow between two coaxial cylinders driven by temperature gradient in the case of specular-diffuse reflection, A modified Nyström-Clenshaw-Curtis quadrature for integral equations with piecewise smooth kernels, Modified filon-Clenshaw-Curtis rules for oscillatory integrals with a nonlinear oscillator, Numerical treatment for solving fractional SIRC model and influenza A, Efficient pricing of Bermudan options using recombining quadratures, Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind, Fast expansion method for evaluating definite integrals with a variable upper limit and a composite or implicitly defined integrand, Numerical analysis of a self-similar turbulent flow in Bose-Einstein condensates, On the positivity and magnitudes of Bayesian quadrature weights, Some error expansions for certain Gaussian quadrature rules, WKB-based scheme with adaptive step size control for the Schrödinger equation in the highly oscillatory regime, A rapid and efficient isogeometric design space exploration framework with application to structural mechanics, Multi-domain spectral approach for the Hilbert transform on the real line, A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling, Indefinite integration of oscillatory functions by the Chebyshev series expansion, Approximation methods for solving fractional optimal control problems, Improving the numerical evaluation of certain oscillatory integrals, On solution of Fredholm integrodifferential equations using composite Chebyshev finite difference method, Chebyshev wavelet finite difference method: a new approach for solving initial and boundary value problems of fractional order, Gauss-Christoffel quadrature for inverse regression: applications to computer experiments, Efficient numerical methods for Cauchy principal value integrals with highly oscillatory integrands, Water wave problem with inclined walls, Generalized block anti-Gauss quadrature rules, Propagation of uncertainties in density-driven flow, Error estimate for a corrected Clenshaw-Curtis quadrature rule, On the quadrature exactness in hyperinterpolation, An improved piecewise variational iteration method for solving strongly nonlinear oscillators, Computation of integrals with oscillatory singular factors of algebraic and logarithmic type, WKB-method for the 1D Schrödinger equation in the semi-classical limit: enhanced phase treatment, Two robust methods for irregular oscillatory integrals over a finite range, Variance reduction in Monte Carlo methods and optimization problems in \({\mathbb{R}}^ n\), A method for efficient computation of integrals with oscillatory and singular integrand, Hilbert and Hadamard transforms by generalized Chebyshev expansion, Numerical solving initial value problem for Fredholm type linear integro-differential equation system, Numerical evaluation of a class of highly oscillatory integrals involving Airy functions, Solution of some types for composition fractional order differential equations corresponding to optimal control problems, Markov-dependent risk model with multi-layer dividend strategy, A sparse grid stochastic collocation upwind finite volume element method for the constrained optimal control problem governed by random convection diffusion equations, A spectral phase-amplitude method for propagating a wave function to large distances, Generalized averaged Gauss quadrature rules for the approximation of matrix functionals, Integral equation method for the continuous spectrum radial Schrödinger equation, Interpolatory quadrature formulae with Chebyshev abscissae of the third or fourth kind, Automatic quadrature on Chebyshev points, A spectral method for the time evolution in parabolic problems, An accurate numerical algorithm for solving singular and nonsingular system of initial value problems on large interval, Multi-element stochastic spectral projection for high quantile estimation, New velocity-space discretization for continuum kinetic calculations and Fokker-Planck collisions, Exponentially convergent Fourier-Chebyshev quadrature schemes on bounded and infinite intervals, Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding, Extended Lagrange interpolation and nonclassical Gauss quadrature formulae, Numerical integration of functions with poles near the interval of integration, Numerical treatment for solving fractional Riccati differential equation, Filon-Clenshaw-Curtis rules for a class of highly-oscillatory integrals with logarithmic singularities, Near-best \(L_1\) approximations on circular and elliptical contours, On the calculation of highly oscillatory integrals with an algebraic singularity, A numerical differentiator, \texttt{Padua2DM}: Fast interpolation and cubature at the Padua points in \texttt{MATLAB/Octave}, On uniform approximations to hypersingular finite-part integrals, Application of high order numerical quadratures to numerical inversion of the Laplace transform, Iterative solution of Volterra integral equations using Clenshaw-Curtis quadrature, Chebyshev finite difference approximation for the boundary value problems, Numerical methods based on rational variable substitution for Wiener-Hopf equations of the second kind, Efficient integration for a class of highly oscillatory integrals, A practical algorithm for computing Cauchy principal value integrals of oscillatory functions, Chebyshev series method for computing weighted quadrature formulas, Filter matrix based on interpolation wavelets for solving Fredholm integral equations, Numerical integration of functions with a sharp peak at or near one boundary using Möbius transformations, The numerical solution of problems in calculus of variation using Chebyshev finite difference method, Modeling transient elastodynamic problems using a novel semi-analytical method yielding decoupled partial differential equations, Weakly nonlinear stability of Hartmann boundary layers, Algorithms for approximating finite Hilbert transform with end-point singularities and its derivatives, Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator, A general framework for solving Riemann-Hilbert problems numerically, Global error bounds for the Clenshaw-Curtis quadrature formula, Efficient computation of Wigner-Eisenbud functions, Chebyshev polynomial solutions of systems of linear integral equations., The numerical evaluation of the error term in a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function, On the Levin iterative method for oscillatory integrals, The Chebyshev fast Gauss and nonuniform fast Fourier transforms and their application to the evaluation of distributed heat potentials, Application of a modified FFT to product type integration, Quadrature formulas of the highest trigonometric accuracy grade and their applications, A high order, progressive method for the evaluation of irregular oscillatory integrals, On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities, Non-intrusive uncertainty quantification using reduced cubature rules, Numerical approximation of oscillatory integrals of the linear ship wave theory, Simplified anti-Gauss quadrature rules with applications in linear algebra, A Chebyshev spectral collocation method for solving Burgers'-type equations, Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs, Numerical solution of Riemann-Hilbert problems: Painlevé II, Sparse pseudospectral approximation method, A spectral fictitious domain method with internal forcing for solving elliptic PDEs, Higher order discontinuous Galerkin method for acoustic pulse problem, Transport cross sections for collisions between particles, An extension of Clenshaw-Curtis quadrature, Chebyshev finite difference method for the solution of boundary-layer equations, Error bounds for approximation in Chebyshev points, Konvergenzbeschleunigung von Cebysev-Entwicklungen, Quadrature formulas for Cauchy principal value integrals, A Bayesian estimation of macro and micro CES production functions, On high precision methods for the evaluation of Fourier integrals with finite and infinite limits, An implicit-Chebyshev pseudospectral method for the effect of radiation on power-law fluid past a vertical plate immersed in a porous medium, Efficient Legendre pseudospectral method for solving integral and integro-differential equations, Comparison of some methods for evaluating infinite range oscillatory integrals, Chebyshev finite difference method for a nonlinear system of second-order boundary value problems, Numerical evaluation of finite Fourier integrals, Product-integration with the Clenshaw-Curtis and related points: Convergence properties, A user-friendly method for computing indefinite integrals of oscillatory functions, Application of the El-Gendi method to the Schrödinger integral equation, Generation of higher order pseudospectral integration matrices, Nontensorial Clenshaw-Curtis cubature, New cubature formulae and hyperinterpolation in three variables, Convergence properties of a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function, Reusing Chebyshev points for polynomial interpolation, An inviscid model for vortex shedding from a deforming body, Product integration with the Clenshaw-Curtis points: Implementation and error estimates, An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures, An adaptive integration scheme for irregularly oscillatory functions, The numerical approximation of a class of finite integrals, Application of adaptive quadrature to axisymmetric vortex sheet motion, Symmetry reduction of Fourier kernels, Uniform approximations to Cauchy principal value integrals of oscillatory functions, New interpolatory quadrature formulae with Chebyshev abscissae, Modified Clenshaw-Curtis method for the computation of Bessel function integrals, Computation of Fourier transform integrals using Chebyshev series expansions, Computing integral transforms and solving integral equations using Chebyshev polynomial approximations, Integral equation method for coupled Schrödinger equations, A plasma resistive diffusion model, An application of the generalized alternating polynomials to the numerical solution of Fredholm integral equations, The Chebyshev points of the first kind, Nyström-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels, On the method for numerical integration of Clenshaw and Curtis, Angenäherte Tschebyscheff-Approximation einer Stammfunktion des Verfahrens von Clenshaw und Curtis, Preconditioning Methods for Thin Scattering Structures Based on Asymptotic Results, A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data, STRATIFIED SEQUENCES OF NESTED QUADRATURE FORMULAS, DOMAIN DECOMPOSITION WITH BEM AND FEM, Numerical treatment for solving fractional logistic differential equation, Accelerating Stochastic Collocation Methods for Partial Differential Equations with Random Input Data, Integrating oscillatory integrands of a non-trigonometric type over a finite range, On High Precision Methods for Computing Integrals Involving Bessel Functions, On a modification of the Clenshaw-Curtis quadrature formula, An efficient discretization scheme for solving nonlinear optimal control problems with multiple time delays, Getting There and Back Again, Numerical inversion of laplace transforms using contour methods, A geometrical interpretation of the addition of nodes to an interpolatory quadrature rule while preserving positive weights, Unnamed Item, The estimation of errors in numerical quadrature, A Fully-Nested Interpolatory Quadrature Based on Fejér’s Second Rule, Error Estimates for the Clenshaw-Curtis Quadrature, Error bounds for the clenshaw-curtis quadrature formulas, ANOTHER NUMERICAL METHOD OF FINDING CRITICAL VALUES FOR THE ANDREWS STABILITY TEST, Proper orthogonal decomposition-based model order reduction via radial basis functions for molecular dynamics systems, The Optimum Addition of Points to Quadrature Formulae, Sparse grids-based stochastic approximations with applications to aerodynamics sensitivity analysis, On Some Gauss and Lobatto Based Integration Formulae, Efficient methods for highly oscillatory integrals with weak and Cauchy singularities, Some methods of numerical integration over a semi-infinite interval, Positivity of the Weights of Extended Clenshaw-Curtis Quadrature Rules, Hypersingular Integrals in Integral Equations and Inequalities: Fundamental Review Study, Multivariate Polynomial Chaos Expansions with Dependent Variables, Stable High Order Quadrature Rules for Scattered Data and General Weight Functions, Fractional Chebyshev Finite Difference Method for Solving the Fractional-Order Delay BVPs, An efficient quadrature rule for weakly and strongly singular integrals, Quadrature formulae of many highly oscillatory Fourier-type integrals with algebraic or logarithmic singularities and their error analysis, Anti-Gaussian quadrature formulas, A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions, APPLICATION OF CLENSHAW–CURTIS METHOD IN CONFINED TIME OF ARRIVAL OPERATOR EIGENVALUE PROBLEM, Solution of non-linear fredholme integral equations by a variational approach, Error Estimates for a Chebyshev Quadrature Method, On the convergence rates of Legendre approximation, Computation of Integrals With Oscillatory and Singular Integrands, Approximation of Laplace transform of fractional derivatives via Clenshaw–Curtis integration, A Sparse Grid Stochastic Collocation Discontinuous Galerkin Method for Constrained Optimal Control Problem Governed by Random Convection Dominated Diffusion Equations, Truncation Errors in Two Chebyshev Series Approximations, Energy Stable Model Order Reduction for the Allen-Cahn Equation, Linear stability of spiral Poiseuille flow with a radial temperature gradient: Centrifugal buoyancy effects, An efficient numerical method to solve inverse fuzzy-uncertain viscoelastic problems of identification, The evaluation of infinite range oscillatory integrals using optimal contours in the complex plane, Computing the Hilbert transform and its inverse, Numerical solution of scattering problems using a Riemann–Hilbert formulation, An Algorithm for Nondominant Solutions of Linear Second-Order Inhomogeneous Difference Equations, Chebyshev functions of half-integer order, The evaluation and application of some modified moments, Combined Shewhart–EWMA control charts with estimated parameters, Pseudospectral integration matrix and boundary value problems, Numerical Evaluation of Some Trigonometric Series, Chebyshev finite difference method for Fredholm integro-differential equation, Stochastic finite element methods for partial differential equations with random input data, A new fractional Chebyshev FDM: an application for solving the fractional differential equations generated by optimisation problem, Unnamed Item, Numerical Quadrature for Bessel Transformations with High Oscillations, A posteriori error estimation for elliptic partial differential equations with small uncertainties, Numerical studies for fractional functional differential equations with delay based on BDF-type shifted Chebyshev approximations, Nonlinear partial differential equations in mathematics and physics, Sequential Stochastic Response Surface Method Using Moving Least Squares-Based Sparse Grid Scheme for Efficient Reliability Analysis, A Chebyshev Finite Difference Method For Solving A Class Of Optimal Control Problems, Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties, Computation of the run-length percentiles of CUSUM control charts under changes in variances, Fehlerabschätzungen für die Quadraturverfahren von Clenshaw und Curtis, Numerical expansion methods for solving Fredholm‐Volterra type linear integral equations by interpolation and quadrature rules, The efficiency of extrapolation methods for numerical integration, A polynomial interpolation process at quasi-Chebyshev nodes with the FFT, The efficient calculation of the transport properties of a dilute gas to a prescribed accuracy, Numerical evaluation of integrals containing a spherical Bessel function by product integration, Error estimates for Clenshaw-Curtis quadrature, Evolution partial differential equations with discontinuous data, Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients, Improved Moving Least Square-Based Multiple Dimension Decomposition (MDD) Technique for Structural Reliability Analysis, Clenshaw-Curtis quadrature with a weighting function, Numerical integration of functions of very many variables, An Efficient, Globally Convergent Method for Optimization Under Uncertainty Using Adaptive Model Reduction and Sparse Grids, Eine Fehlerabschätzung zum Quadraturverfahren von Clenshaw und Curtis, Numerical scattering for the defocusing Davey–Stewartson II equation for initial data with compact support, An automatic integration procedure for infinite range integrals involving oscillatory kernels, A numerical technique for solving fractional variational problems, Solution of linear optimal control problems with time delay using a composite Chebyshev finite difference method, An extrapolation procedure for the evaluation of singular integrals, An expansion method for irregular oscillatory integrals, Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations., The iterative solution of a nonlinear fredholm integral equation arising from a chemical reactor problem, Non-intrusive Uncertainty Propagation with Error Bounds for Conservation Laws Containing Discontinuities, Numerical expansion methods for solving systems of linear integral equations using interpolation and quadrature rules, On the secondary flow induced by spheres and discs rotating in elastico-viscous liquids, Legendre spectral method for solving integral and integro-differential equations, Exactness of Quadrature Formulas, Exploring emerging manycore architectures for uncertainty quantification through embedded stochastic Galerkin methods, Application of local improvements to reduced-order models to sampling methods for nonlinear PDEs with noise, Robust spectral method for numerical valuation of european options under Merton's jump‐diffusion model, Decoupled scaled boundary finite element method for analysing dam–reservoir dynamic interaction, Fast algorithms using orthogonal polynomials, Linear response analysis of supersonic turbulent channel flows with a large parameter space, A numerical method for the integration of oscillatory functions, On numerical approaches to nonlinear Schrödinger and Korteweg-de Vries equations for piecewise smooth and slowly decaying initial data, An automatic quadrature method for semi-infinite integrals of exponentially decaying functions and its Matlab code, An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use, Highly accurate quadrature-based scharfetter-gummel schemes for charge transport in degenerate semiconductors, An adaptive virtual element method for the polymeric self-consistent field theory, Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs, Adaptive integration of convex functions of one real variable, Boundary element analysis of 3D shell‐like rigid electrically conducting inclusions in anisotropic thermomagnetoelectroelastic solids, Parallel numerical Picard iteration methods, Efficient adaptive stochastic collocation strategies for advection-diffusion problems with uncertain inputs, Numerical modelling of advection diffusion equation using Chebyshev spectral collocation method and Laplace transform, Iterative Processes and Integral Equations of the Second Kind, A quadrature rule of interpolatory type for Cauchy integrals, A quadrature rule for weighted Cauchy integrals, A trigonometric quadrature rule for Cauchy integrals with Jacobi weight, On Interpolation Approximation: Convergence Rates for Polynomial Interpolation for Functions of Limited Regularity, A new family of extended Gauss quadratures with an interior interval constraint, A Chebyshev quadrature rule for one sided finite part integrals, Interpolatory quadrature formulae with Chebyshev abscissae, Optimal systems of nodes for Lagrange interpolation on bounded intervals. A survey, The nonlinear evolution of vortex sheets with surface tension in axisymmetric flows, The Evaluation and Estimation of the Coefficients in the Chebyshev Series Expansion of a Function
Cites Work
