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On Calculating with B-Splines II. Integration

  • Carl de Boor
  • Tom Lyche
  • Larry L. Schumaker
Part of the International Series of Numerical Mathematics book series (ISNM, volume 30)

Abstract

This paper is a continuation of the paper [1] of the same name by the first author in which it is shown how values of B-splines and their derivatives can be computed by stable algorithms based on recursions involving only convex combinations of nonnegative quantities (cf. also Cox [3]). In this paper we consider integrals of B-splines and of B-spline series. In addition, we derive recursions for the computation of integrals of products of B-splines (of possibly different orders and on possibly different knot sequences). As an application, we consider the numerical computation of the Gram matrix which arises in least squares fitting using B-splines.

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Copyright information

© Springer Basel AG 1976

Authors and Affiliations

  • Carl de Boor
    • 1
  • Tom Lyche
    • 2
  • Larry L. Schumaker
    • 3
  1. 1.Mathematics Research CenterUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsUniversity of OsloOslo 3Norway
  3. 3.Department of MathematicsUniversity of TexasAustinUSA

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