Computation of Gauss-type quadrature formulas |
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Affiliation: | School for Modelling Sciences, Potchefstroomse Universiteit vir CHO, Vaal Triangle Campus, P.O. Box 1174 Vanderbijlpark, South Africa |
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Abstract: | Gaussian formulas for a linear functional L (such as a weighted integral) are best computed from the recursion coefficients relating the monic polynomials orthogonal with respect to L. In Gauss-type formulas, one or more extraneous conditions (such as pre-assigning certain nodes) replace some of the equations expressing exactness when applied to high-order polynomials. These extraneous conditions may be applied by modifying the same number of recursion coefficients. We survey the methods of computing formulas from recursion coefficients, methods of obtaining recursion coefficients and modifying them for Gauss-type formulas, and questions of existence and numerical accuracy associated with those computations. |
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