Gautschi, Walter High-order generalized Gauss-Radau and Gauss-Lobatto formulae for Jacobi and Laguerre weight functions. (English) Zbl 1167.65347 Numer. Algorithms 51, No. 2, 143-149 (2009). 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 \(1,000\). Cited in 6 Documents MSC: 65D32 Numerical quadrature and cubature formulas 41A55 Approximate quadratures Keywords:high-order generalized Gauss-Radau and Gauss-Lobatto quadrature formulae; Jacobi weight functions; Laguerre weight functions Software:OPQ; HOGGRL PDFBibTeX XMLCite \textit{W. Gautschi}, Numer. Algorithms 51, No. 2, 143--149 (2009; Zbl 1167.65347) Full Text: DOI References: [1] Gautschi, W.: High-order Gauss–Lobatto formulae. Numer. Algorithms 25, 213–222 (2000) · Zbl 0979.65021 · doi:10.1023/A:1016689830453 [2] Gautschi, W.: Orthogonal Polynomials: Computation and Approximation. Oxford University Press, Oxford (2004) · Zbl 1130.42300 [3] Gautschi, W.: Generalized Gauss–Radau and Gauss–Lobatto formulae. BIT Numer. Math. 44, 711–720 (2004) · Zbl 1076.65023 · doi:10.1007/s10543-004-3812-0 [4] Gautschi, W., Li, S.: Gauss–Radau and Gauss–Lobatto quadratures with double end points. J. Comput. Appl. Math. 34, 343–360 (1991) · Zbl 0727.65012 · doi:10.1016/0377-0427(91)90094-Z [5] Golub, G.H.: Some modified matrix eigenvalue problems. SIAM Rev. 15, 318–334 (1973) · Zbl 0254.65027 · doi:10.1137/1015032 [6] Szegö, G.: Orthogonal Polynomials, 4th edn. American Mathematical Society Colloquium Publications 23. American Mathematical Society, Providence (1978) · JFM 65.0278.03 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.