On calculation of scalar products of $B$-splines

A. I. Rozhenko

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: The paper is devoted to algorithms of stable calculation of scalar products of $B$-splines. A new modification of recursive calculations of integrals in the Gram matrix is proposed. The modified algorithm is nearly two times faster than the Gauss quadratures and the full recursion algorithm.

Key words: $B$-spline, divided difference, the Gram matrix.

UDC: 519.6

Received: 11.10.2004
Revised: 14.09.2005

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