Generalized averaged Gauss quadrature rules for the approximation of matrix functionals
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- 作者：Lothar Reichel ; Miodrag M. Spalević ; Tunan Tang
- 关键词：Matrix functional ; Gauss quadrature ; Averaged Gauss rules
- 刊名：BIT Numerical Mathematics
- 出版年：2016
- 出版时间：September 2016
- 年：2016
- 卷：56
- 期：3
- 页码：1045-1067
- 全文大小：576 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Computational Mathematics and Numerical Analysis
Numeric Computing
Mathematics - 出版者：Springer Netherlands
- ISSN：1572-9125
- 卷排序：56
文摘
The need to compute expressions of the form \(u^*f(A)v\), where A is a large square matrix, u and v are vectors, and f is a function, arises in many applications, including network analysis, quantum chromodynamics, and the solution of linear discrete ill-posed problems. Commonly used approaches first reduce A to a small matrix by a few steps of the Hermitian or non-Hermitian Lanczos processes and then evaluate the reduced problem. This paper describes a new method to determine error estimates for computed quantities and shows how to achieve higher accuracy than available methods for essentially the same computational effort. Our methods are based on recently proposed generalized averaged Gauss quadrature formulas.