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On Some General Lacunary Interpolation Problems

✍ Scribed by A. Sharma; J. Szabados; B. Underhill; A.K. Varma

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
700 KB
Volume
87
Category
Article
ISSN
0021-9045

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✦ Synopsis

The object of this paper is to give a unified and complete treatment of these related cases of lacunary interpolation whose special cases can be found scattered in the literature. We consider only the case when the nodes are the zeros of ? n (x) whose derivative is &n(n&1) P n&1 (x), the Legendre polynomial of degree n&1. We find the fundamental polynomials and give the convergence results.

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We consider at first a (0,4) lacunary interpolation problem, and we solve it in an appropriate class of "deficient" splines. Under suitable assumptions, we show existence and uniqueness of the solution. We provide the convergence analysis, showing that the method is of order "almost" five. Some addi