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High-order generalized Gauss-Radau and Gauss-Lobatto formulae for Jacobi and Laguerre weight functions. (English) Zbl 1167.65347

Summary: The generation of generalized Gauss-Radau and Gauss-Lobatto quadrature formulae by methods developed by us earlier breaks down in the case of Jacobi and Laguerre measures when the order of the quadrature rules becomes very large. The reason for this is underflow resp. overflow of the respective monic orthogonal polynomials. By rescaling of the polynomials, and other corrective measures, the problem can be circumvented, and formulae can be generated of orders as high as \(1,000\).

MSC:

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures

Software:

OPQ; HOGGRL
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Full Text: DOI

References:

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