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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References
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de Boor, C., Lyche, T., Schumaker, L.L. (1976). On Calculating with B-Splines II. Integration. In: Collatz, L., Werner, H., Meinardus, G. (eds) Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory. International Series of Numerical Mathematics, vol 30. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7692-6_6
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DOI: https://doi.org/10.1007/978-3-0348-7692-6_6
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