Journal
MATHEMATICS OF COMPUTATION
Volume 82, Issue 284, Pages 2035-2060Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-2013-02695-6
Keywords
Extended Krylov subspace; orthogonal Laurent polynomial; recursion relation; matrix functional; rational Gauss quadrature
Categories
Funding
- Hanover College Faculty Development Committee
- NSF [DMS-1115385]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1115385] Funding Source: National Science Foundation
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available