On Linear Spline Wavelets with Shifted Supports

Svetlana Makarova, Anton Makarov

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

1 Scopus citations

Abstract

We examine Faber’s type decompositions for spaces of linear minimal splines constructed on nonuniform grids on a segment. A characteristic feature of the Faber decomposition is that the basis wavelets are centered around the knots that do not belong to the coarse grid. The construction of the lazy wavelets begins with the use of the basis functions in refined spline space centered at the odd knots. We propose to use as wavelets the functions centered at the even knots under some conditions. In contrast to lazy wavelets, in this case the decomposition system of equations has a unique solution, which can be found by the sweep method with the guarantee of well-posedness and stability.

Original languageEnglish
Title of host publicationNumerical Computations: Theory and Algorithms
EditorsYaroslav D. Sergeyev, Dmitri E. Kvasov, Yaroslav D. Sergeyev, Dmitri E. Kvasov
Place of PublicationCham
PublisherSpringer Nature
Pages430-437
ISBN (Print)9783030406158
DOIs
StatePublished - 2020
Event3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019 - Crotone, Italy
Duration: 15 Jun 201921 Jun 2019

Publication series

NameLecture Notes in Computer Science
Volume11974
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019
CountryItaly
CityCrotone
Period15/06/1921/06/19

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Keywords

  • B-spline
  • Minimal splines
  • Nonuniform grid
  • Wavelets

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