Banded matrices with banded inverses. II: Locally finite decomposition of spline spaces

DOI10.1007/BF01198006zbMath0784.15005OpenAlexW1984171200MaRDI QIDQ1801490

Wolfgang Dahmen, Charles A. Micchelli

Publication date: 6 April 1994

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01198006

zbMATH Keywords

wavelets\(B\)-splinesmatrix equationstotal positivityToeplitz matricesmatrix factorizationmultiscale methodsspline spacesHurwitz matricestwo-slanted matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Matrix equations and identities (15A24) Equations involving linear operators, with operator unknowns (47A62) General harmonic expansions, frames (42C15) Spline approximation (41A15) Matrix and operator functional equations (39B42)

Related Items (16)

Nonstationary tight wavelet frames. I: Bounded intervals ⋮ Elementary factorisation of box spline subdivision ⋮ On the matrix completion problem for multivariate filter bank construction ⋮ Recursive properties of Toeplitz and Hurwitz matrices ⋮ Construction of optimally conditioned cubic spline wavelets on the interval ⋮ On the invertibility of ``rectangular bi-infinite matrices and applications in time-frequency analysis ⋮ Cubic spline wavelets with complementary boundary conditions ⋮ A construction of \(C^1\)-wavelets on the two-dimensional sphere ⋮ New stable biorthogonal spline-wavelets on the interval ⋮ A multiresolution analysis for tensor-product splines using weighted spline wavelets ⋮ Factoring wavelet transforms into lifting steps ⋮ Wavelet transforms that map integers to integers ⋮ Biorthogonal spline wavelets on the interval -- stability and moment conditions ⋮ Reversing subdivision rules: Local linear conditions and observations on inner products ⋮ Fast Algorithms for Adaptive Free Knot Spline Approximation Using Nonuniform Biorthogonal Spline Wavelets ⋮ Decomposition of refinable spaces and applications to operator equations

Cites Work

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• Total positivity of the discrete spline collocation matrix
• Using the refinement equation for the construction of pre-wavelets
• Stationary subdivision
• On Refinement Equations Determined by Pólya Frequency Sequences
• Inverses of Band Matrices and Local Convergence of Spline Projections

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