The structure of matrices in rational Gauss quadrature
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Abstract:
This paper is concerned with the approximation of matrix functionals defined by a large, sparse or structured, symmetric definite matrix. These functionals are Stieltjes integrals with a measure supported on a compact real interval. Rational Gauss quadrature rules that are designed to exactly integrate Laurent polynomials with a fixed pole in the vicinity of the support of the measure may yield better approximations of these functionals than standard Gauss quadrature rules with the same number of nodes. Therefore it can be attractive to approximate matrix functionals by these rational Gauss rules. We describe the structure of the matrices associated with these quadrature rules, derive remainder terms, and discuss computational aspects. Also discussed are rational Gauss-Radau rules and the applicability of pairs of rational Gauss and Gauss-Radau rules to computing lower and upper bounds for certain matrix functionals.References
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Additional Information
- Carl Jagels
- Affiliation: Department of Mathematics and Computer Science, Hanover College, Hanover, Indiana 47243
- Email: jagels@hanover.edu
- Lothar Reichel
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- Email: reichel@math.kent.edu
- Received by editor(s): August 15, 2011
- Received by editor(s) in revised form: February 27, 2012
- Published electronically: April 9, 2013
- Additional Notes: This research was supported in part by a grant from the Hanover College Faculty Development Committee
This research was supported in part by NSF grant DMS-1115385 - © Copyright 2013 American Mathematical Society
- Journal: Math. Comp. 82 (2013), 2035-2060
- MSC (2010): Primary 65F25, 65F60, 65D32
- DOI: https://doi.org/10.1090/S0025-5718-2013-02695-6
- MathSciNet review: 3073191