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

Authors:
T. N. L. Patterson
Affiliations:
Queen's Univ. of Belfast, Belfast, Northern Ireland
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1989

Citing 2
Cited 2

Algorithm 468: algorithm for automatic numerical integration over a finite interval [D1]

Communications of the ACM
A generalized Bairstow algorithm

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Algorithm 672: generation of interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions

ACM Transactions on Mathematical Software (TOMS)
Algorithm 699: a new representation of Patterson's quadrature formulae

ACM Transactions on Mathematical Software (TOMS)

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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.