Construction of splines of maximal smoothness

We consider approximation relations as a system of linear algebraic equations and obtain spaces of minimal Lagrange type splines of arbitrary order. Using an analog of procedure for constructing elementary symmetric polynomials, we obtain new explicit formulas for representing splines. The splines o...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 178; no. 6; pp. 589 - 604
Main Author Makarov, A. A.
Format Journal Article
LanguageEnglish
Published Boston Springer US 02.11.2011
Springer
Subjects
Mathematics
Mathematics and Statistics
Wavelet Decomposition
Approximation Relation
Arbitrary Order
Grid Point
Nonuniform Grid
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Summary:We consider approximation relations as a system of linear algebraic equations and obtain spaces of minimal Lagrange type splines of arbitrary order. Using an analog of procedure for constructing elementary symmetric polynomials, we obtain new explicit formulas for representing splines. The splines obtained possess the maximal smoothness and minimal compact support. We also give examples of constructing splines on an open interval and on a segment. Bibliography: 15 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-011-0572-7