Convergence of vector subdivision schemes in Sobolev spaces

DOI10.1006/acha.2001.0363zbMath1006.65153OpenAlexW2092896986MaRDI QIDQ1604501

Rong-Qing Jia, Di-Rong Chen, Sherman D. Riemenschneider

Publication date: 4 July 2002

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/b3ec7af95190b4414f119111662b58548ca73ac7

zbMATH Keywords

waveletsSobolev spacemultiresolution analysisvector subdivision schemeeigenvalue conditioncascade algortihm

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Numerical methods for wavelets (65T60)

Related Items (46)

Approximation order and approximate sum rules in subdivision ⋮ Riesz multiwavelet bases ⋮ Convergence rates of cascade algorithms ⋮ Complete characterization of the regions of \(C^2\) and \(C^3\) convergence of combined ternary 4-point subdivision schemes ⋮ Solutions of multiple vector refinement equations with infinite mask ⋮ Multivariate refinable Hermite interpolant ⋮ A construction of multiresolution analysis on interval ⋮ Vector subdivision schemes and their convergence for arbitrary matrix masks ⋮ Convergence and error estimate of cascade algorithms with infinitely supported masks in \(L_p(\mathbb R^s)\) ⋮ Vector cascade algorithms with infinitely supported masks in weighted \(L_2\)-spaces ⋮ Decompositions of trigonometric polynomials with applications to multivariate subdivision schemes ⋮ \(L_p\)-solutions of vector refinement equations with general dilation matrix ⋮ Vector cascade algorithms and refinable function vectors in Sobolev spaces ⋮ Multiple multivariate subdivision schemes: matrix and operator approaches ⋮ Polynomial reproduction of vector subdivision schemes ⋮ Vector multivariate subdivision schemes: comparison of spectral methods for their regularity analysis ⋮ Finiteness conjecture and subdivision ⋮ A CONSTRUCTION OF CONVERGENT CASCADE ALGORITHMS IN SOBOLEV SPACES ⋮ Convergence rate of vector subdivision scheme ⋮ Limits of level and parameter dependent subdivision schemes: a matrix approach ⋮ Biorthogonal multiple wavelets generated by vector refinement equation ⋮ Convergence of wavelet thresholding estimators of differential operators ⋮ Vector refinement equations with infinitely supported masks ⋮ Regularity of non-stationary subdivision: a matrix approach ⋮ Subdivisions with infinitely supported mask ⋮ Subdivision schemes with polynomially decaying masks ⋮ Convergence of subdivision schemes and smoothness of limit functions ⋮ On the regularity analysis of interpolatory Hermite subdivision schemes ⋮ Concerning order of convergence for subdivision ⋮ Regularity of multivariate vector subdivision schemes ⋮ Jet subdivision schemes on the \(k\)-regular complex ⋮ The independence of initial vectors in the subdivision schemes ⋮ Joint spectral radius and ternary Hermite subdivision ⋮ Interpolating \(m\)-refinable functions with compact support: the second generation class ⋮ A generalization of the mean size formula of wavelet packets in \(L_p\) ⋮ Optimal $C^2$ two-dimensional interpolatory ternary subdivision schemes with two-ring stencils ⋮ Tangents and curvatures of matrix-valued subdivision curves and their applications to curve design ⋮ Convergence rates of cascade algorithms associated with nonhomogeneous refinement equations ⋮ Analysis and construction of multivariate interpolating refinable function vectors ⋮ Regularity of anisotropic refinable functions ⋮ Pointwise convergence of bounded cascade sequences ⋮ Convergence rates of vector cascade algorithms in \(L_p\) ⋮ Convergence of cascade algorithms by frequency approach ⋮ Stability implies convergence of cascade algorithms in Sobolev space ⋮ Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks ⋮ Subdivision schemes, network flows and linear optimization

Cites Work

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• Subdivision schemes in \(L_ p\) spaces
• Convergence of nonstationary cascade algorithms
• Stationary subdivision
• Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
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• Vector subdivision schemes and multiple wavelets
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• Approximation properties of multivariate wavelets
• Approximation by Multiple Refinable Functions
• Approximation orders of FSI spaces in \(L_2(\mathbb{R}^d)\)

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