Regularity of multivariate vector subdivision schemes

DOI10.1007/s11075-004-3623-zzbMath1071.65019OpenAlexW2036294355MaRDI QIDQ1776171

Maria Charina, Thomas Sauer, Constanza Conti

Publication date: 20 May 2005

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-004-3623-z

zbMATH Keywords

convergencedifference schemedifference operatormulti-waveletsvector subdivision schemerestricted spectral radiusrefinement maskmatrix subdivision scheme

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (31)

Approximation order and approximate sum rules in subdivision ⋮ A shape preserving \(C^2\) non-linear, non-uniform, subdivision scheme with fourth-order accuracy ⋮ A constructive algebraic strategy for interpolatory subdivision schemes induced by bivariate box splines ⋮ Multivariate generalized Hermite subdivision schemes ⋮ Multivariate compactly supported \(C^\infty\) functions by subdivision ⋮ Analysis and convergence of Hermite subdivision schemes ⋮ Elliptic polytopes and invariant norms of linear operators ⋮ System theory and orthogonal multi-wavelets ⋮ Multiple multivariate subdivision schemes: matrix and operator approaches ⋮ Analysis of non-stationary Hermite subdivision schemes reproducing exponential polynomials ⋮ Vector multivariate subdivision schemes: comparison of spectral methods for their regularity analysis ⋮ Dual Hermite subdivision schemes of de Rham-type ⋮ Factorization of Hermite subdivision operators from polynomial over-reproduction ⋮ Extended Hermite subdivision schemes ⋮ Smoothed hat functions in subdivision ⋮ Regularity of non-stationary subdivision: a matrix approach ⋮ Construction of Hermite subdivision schemes reproducing polynomials ⋮ Full rank interpolatory subdivision: a first encounter with the multivariate realm ⋮ Scalar multivariate subdivision schemes and box splines ⋮ Unnamed Item ⋮ Regularity of multivariate vector subdivision schemes ⋮ An annihilator-based strategy for the automatic detection of exponential polynomial spaces in subdivision ⋮ Subdivision Schemes and Norms ⋮ Joint spectral radius and ternary Hermite subdivision ⋮ A new family of non-stationary Hermite subdivision schemes reproducing exponential polynomials ⋮ Data-driven extrapolation via feature augmentation based on variably scaled thin plate splines ⋮ Non-stationary subdivision schemes: state of the art and perspectives ⋮ $C^1$ Analysis of Hermite Subdivision Schemes on Manifolds ⋮ Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes ⋮ A shape preserving corner cutting algorithm with an enhanced accuracy ⋮ Subdivision schemes, network flows and linear optimization

Cites Work

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• On vector subdivision
• On existence and weak stability of matrix refinable functions
• Biorthogonal wavelet expansions
• Regularity of multiwavelets
• Vector cascade algorithms and refinable function vectors in Sobolev spaces
• Convergence of vector subdivision schemes in Sobolev spaces
• Regularity of multivariate vector subdivision schemes
• Subdivision schemes in \(L_ p\) spaces
• Subdivision schemes in geometric modelling
• Stationary subdivision
• Multivariate Refinement Equations and Convergence of Subdivision Schemes
• Vector subdivision schemes and multiple wavelets
• Multivariate matrix refinable functions with arbitrary matrix dilation
• Refinable Function Vectors
• Polynomial interpolation, ideals and approximation order of multivariate refinable functions
• Smoothness of Multiple Refinable Functions and Multiple Wavelets

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