An algorithm for generating interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions

Author:

Patterson T. N. L.1

Affiliation:

1. Queen's Univ. of Belfast, Belfast, Northern Ireland

Abstract

The construction of an algorithm is described for generating interpolatory quadrature rules of the highest degree of precision with arbitrarily preassigned nodes for general constant signed weight functions. It is of very wide application in that to operate, only the definition of the 3-term recurrence relation for the orthogonal polynomials associated with the weight function need be supplied. The algorithm can be used to produce specific individual quadrature rules or sequences of rules by iterative application.

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

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