This article is cited in 9 papers

The inverses of cyclic band matrices and the convergence of interpolation processes for derivatives of periodic interpolation splines

Yu. S. Volkov<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Novosibirsk

Abstract: The estimates for entries of matrices inverse to the cyclic band matrices and for the matrix norms are presented. The results obtained are used for determining the convergence conditions of Interpolation processes by periodic odd degree splines for different derivatives. In particular, the positive solution to the C. de Boor problem on unconditional convergence of one of the two middle derivatives in the periodic case is proposed.

Key words: banded matrix, cyclic banded matrix, inverse matrix, norm of matrix, spline, interpolation, convergence.

UDC: 519.65

Received: 15.09.2009
Revised: 17.11.2009

 English version: Numerical Analysis and Applications, 2010, 3:3, 199–207

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