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Numerical methods and programming, 2012, Volume 13, Issue 1, Pages 74–86 (Mi vmp10)  
This article is cited in 1 scientific paper (total in 1 paper)

Вычислительные методы и приложения

Knot insertion and knot removal matrices for nonpolynomial splines

A. A. Makarov

St. Petersburg State University, Department of Mathematics and Mechanics
Full-text PDF (230 kB) Citations (1)
Abstract: Continuously differentiable splines of second order on a nonuniform grid are constructed. Formulas of polynomial and nonpolynomial (trigonometric and hyperbolic) are given. Calibration relations expressing the coordinate splines on the original grid as a linear combination of splines of the same type on a refined grid and calibration relations representing the coordinate splines on an enlarged grid as a linear combination of splines of the same type on the original grid are obtained. Knot insertion and knot removal matrices on an interval and on a segment for splines associated with infinite and finite nonuniform grids respectively are constructed.
Keywords: spline; wavelet; biorthogonal systems; decomposition matrix; reconstruction matrix; subdivision scheme; knot insertion and removal algorithms; spline curve.
Received: 25.10.2011
Document Type: Article
UDC: 519.6
Language: Russian
Citation: A. A. Makarov, “Knot insertion and knot removal matrices for nonpolynomial splines”, Num. Meth. Prog., 13:1 (2012), 74–86
Citation in format AMSBIB
\Bibitem{Mak12}
\by A.~A.~Makarov
\paper Knot insertion and knot removal matrices for nonpolynomial splines
\jour Num. Meth. Prog.
\yr 2012
\vol 13
\issue 1
\pages 74--86
\mathnet{http://mi.mathnet.ru/vmp10}
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  • https://www.mathnet.ru/eng/vmp/v13/i1/p74
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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