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 in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2011-11, Vol.178 (6), p.589-604
Main Author: Makarov, A. A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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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