Biorthogonal spline wavelets on the interval -- stability and moment conditions
From MaRDI portal
Publication:1283558
DOI10.1006/acha.1998.0247zbMath0922.42021OpenAlexW2064216226MaRDI QIDQ1283558
Angela Kunoth, Karsten Urban, Wolfgang Dahmen
Publication date: 21 September 1999
Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/acha.1998.0247
numerical stabilitybiorthogonal waveletsRiesz basesBernstein inequalitiesmoment conditionsdiscrete Sobolev normsJackson estimatesmultiresolution analysis on the interval
Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Spline approximation (41A15)
Related Items
Low-rank tensor methods for partial differential equations, Computing eigenelements of Sturm-Liouville problems by using Daubechies wavelets, Multilevel a posteriori error analysis for reaction-convection-diffusion problems, Cubic spline wavelets with short support for fourth-order problems, Multiresolution weighted norm equivalencies and applications, Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions, WAVELETS ON THE INTERVAL WITH OPTIMAL LOCALIZATION, A REALIZATION OF A WAVELET GALERKIN METHOD ON NONTRIVIAL DOMAINS, A minimal search method for solving fractional integro-differential equations based on modified Legendre multiwavelets, Application of the sinc method to a dynamic elasto-plastic problem, The approximate inverse in action II: convergence and stability, Finite element wavelets with improved quantitative properties, Efficient application of nonlinear stationary operators in adaptive wavelet methods -- the isotropic case, Construction of wavelets and framelets on a bounded interval, Implementation of the mortar method in the wavelet context, A wavelet Galerkin method for the Stokes equations, Adaptive wavelet methods on unbounded domains, Piecewise tensor product wavelet bases by extensions and approximation rates, Multivariate intensity estimation via hyperbolic wavelet selection, Dirichlet Forms and Finite Element Methods for the SABR Model, Anisotropic curl-free wavelets with boundary conditions, Construction of dual multiple knot B-spline wavelets on interval, Divergence-free wavelet bases on the hypercube, Moment preserving local spline projection operators, Adaptive wavelet methods for linear and nonlinear least-squares problems, Construction of optimally conditioned cubic spline wavelets on the interval, Stable, linear spline wavelets on nonuniform knots with vanishing moments, On the exact values of coefficients of coiflets, Adaptive piecewise tensor product wavelets scheme for Laplace-interface problems, An adaptive wavelet method for nonlinear partial differential equations with applications to dynamic damage modeling, Anisotropic curl-free wavelet bases on the unit cube, Optimal space-time adaptive wavelet methods for degenerate parabolic PDEs, Scientific computing in electrical engineering SCEE 2010. Selected papers based on the presentations at the 8th conference, Toulouse, France, September 2010., ON THE COMPUTATION OF GRAMIAN MATRICES FOR REFINABLE BASES ON THE INTERVAL, Wavelet bases in $\mathbf{H}( \mathrm{div})$ and $\mathbf{H}(\mathbf{curl})$, Construction of finite-dimensional multiresolutions based on linear subdivision schemes: application to the 4-point shifted Lagrange scheme, Quadratic spline wavelets with arbitrary simple knots on the sphere., Optimal convergence rates for sparsity promoting wavelet-regularization in Besov spaces, Cubic spline wavelets with four vanishing moments on the interval and their applications to option pricing under Kou model, Stabilized wavelet approximations of the Stokes problem, Postprocessing Galerkin method using quadratic spline wavelets and its efficiency, Uniformly stable wavelets on nonuniform triangulations, A wavelet-based nested iteration-inexact conjugate gradient algorithm for adaptively solving elliptic PDEs, The wavelet element method. II: Realization and additional features in 2D and 3D, Wavelet compression of anisotropic integrodifferential operators on sparse tensor product spaces, Wavelet-Galerkin method for second-order integro-differential equations on product domains, The Construction of Orthonormal Wavelets Using Symbolic Methods and a Matrix Analytical Approach for Wavelets on the Interval, Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and application to free-slip divergence-free wavelets, Adaptive wavelet frame domain decomposition methods for nonlinear elliptic equations, SPLINE WAVELETS WITH BOUNDARY VALUES AND VANISHING MOMENTS, Quadratic spline wavelets with short support satisfying homogeneous boundary conditions, Biorthogonal multiwavelets on the interval for numerical solutions of Burgers' equation, AN OPERATOR SPLITTING PRECONDITIONER FOR MATRICES ARISING FROM A WAVELET BOUNDARY ELEMENT METHOD FOR THE HELMHOLTZ EQUATION, Adaptive wavelet methods using semiorthogonal spline wavelets: Sparse evaluation of nonlinear functions, Divergence-free wavelet bases on the hypercube: Free-slip boundary conditions, and applications for solving the instationary Stokes equations, Riesz bases of wavelets and applications to numerical solutions of elliptic equations, Fast methods for three-dimensional inverse obstacle scattering problems, Cubic spline wavelets with complementary boundary conditions, Optimality of adaptive Galerkin methods for random parabolic partial differential equations, A construction of \(C^1\)-wavelets on the two-dimensional sphere, Adaptive frame methods for nonlinear variational problems, Spatial approximation of stochastic convolutions, Numerical methods for Lévy processes, Wavelet methods for PDEs -- some recent developments, New stable biorthogonal spline-wavelets on the interval, Quadratic spline wavelets with short support for fourth-order problems, Optimal extensions on tensor-product meshes, Recent results on wavelet bases on the interval generated by GP refinable functions, Wavelet preconditioning for the three fields formulation: Numerical results in conforming decomposition, Adaptive application of operators in standard representation, Adaptive wavelet algorithms for elliptic PDE's on product domains, Using divergence-free wavelets for the numerical solution of the 2-D stationary Navier-Stokes equations, The Mortar Method in the Wavelet Context, Adaptive wavelet schemes for an elliptic control problem with Dirichlet boundary control, A multiresolution analysis for tensor-product splines using weighted spline wavelets, Fast iterative solution of elliptic control problems in wavelet discretization, Adaptive application of the operator exponential, Space-time adaptive wavelet methods for parabolic evolution problems, Linear complexity solution of parabolic integro-differential equations, Preparation of CAD and Molecular Surfaces for Meshfree Solvers, Multilevel Preconditioning for Variational Problems, Iterative algorithms for multiscale state estimation. I: Concepts, Adaptive frame methods for nonlinear elliptic problems, Adaptive frame methods for elliptic operator equations, Wavelets on intervals derived from arbitrary compactly supported biorthogonal multiwavelets, Fast diffusion wavelet method for partial differential equations, On the unification of schemes and software for wavelets on the interval, Wavelets on manifolds: An optimized construction, Nonlinear and adaptive frame approximation schemes for elliptic PDEs: Theory and numerical experiments, Galerkin method with new quadratic spline wavelets for integral and integro-differential equations, Wavelets with complementary boundary conditions -- functions spaces on the cube, The wavelet element method. I: Construction and analysis, Derivative-orthogonal Riesz wavelets in Sobolev spaces with applications to differential equations, Wavelets with patchwise cancellation properties, Samplets: construction and scattered data compression, Fast Algorithms for Adaptive Free Knot Spline Approximation Using Nonuniform Biorthogonal Spline Wavelets, Wavelet characterizations for anisotropic Besov spaces, Numerical analysis of semilinear stochastic evolution equations in Banach spaces, Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients, Derivative-orthogonal wavelets for discretizing constrained optimal control problems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Total positivity of the discrete spline collocation matrix
- On the numerical condition of polynomials in Bernstein form
- Ondelettes sur l'intervalle. (Wavelets on the interval)
- Multilevel preconditioning
- Nonorthogonal multiresolution analyses, commutation between projectors and differentiation and divergence-free vector wavelets
- A practical guide to splines
- Wavelets on the interval and fast wavelet transforms
- Wavelet approximation methods for pseudodifferential equations. I: Stability and convergence
- Biorthogonal multiresolution analysis on the interval and applications
- Stability of multiscale transformations
- Banded matrices with banded inverses. II: Locally finite decomposition of spline spaces
- On divergence-free wavelets
- Multilevel preconditioning -- appending boundary conditions by Lagrange multipliers
- Wavelet approximation methods for pseudodifferential equations. II: Matrix compression and fast solution
- On total positivity of the discrete spline collocation matrix
- A wavelet Galerkin method for the Stokes equations
- Local decomposition of refinable spaces and wavelets
- Non-separable bidimensional wavelet bases
- Fast wavelet transforms and numerical algorithms I
- Spline bases in classical function spaces on compact $C^{∞}$ manifolds, Part I
- Interpolation of Besov Spaces
- Multidimensional Spline Approximation
- Stationary subdivision
- Biorthogonal bases of compactly supported wavelets
- Real Interpolation of Sobolev Spaces on Subdomains of Rn
- Multiscale decompositions on bounded domains
- Using the Refinement Equation for Evaluating Integrals of Wavelets
- BIORTHOGONAL SPLINE WAVELETS ON THE INTERVAL FOR THE RESOLUTION OF BOUNDARY PROBLEMS
- Numerical stability of biorthogonal wavelet transforms