Generalized averaged Gauss quadrature rules for the approximation of matrix functionals
Generalized averaged Gauss quadrature rules for the approximation of matrix functionals
复制标题
矩阵泛函近似的广义平均高斯求积规则
DOI：
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复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Tunan Tang
中科院分区：
文献类型：
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作者：
L. Reichel;M. Spalević;Tunan Tang
在许多应用中，包括网络分析、量子色动力学和线性离散不适定问题的求解，都需要计算形式为$$u^*f(A)v$$u∗f(A)v的表达式，其中A是大方阵，u和v是向量，f是函数。常用的方法首先通过埃尔米特或非埃尔米特Lanczos过程的几个步骤将A缩减为一个小矩阵，然后评估简化后的问题。本文描述了一种确定计算量误差估计的新方法，并展示了在基本相同的计算量下如何获得比现有方法更高的精度。我们的方法是基于最近提出的广义平均高斯求积公式。
The need to compute expressions of the form $$u^*f(A)v$$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.
DOI：
10.1016/j.physa.2008.11.011
发表时间：
2009-03-01
影响因子：
3.3
作者：
Estrada, Ernesto;Higham, Desmond J.;Hatano, Naomichi
通讯作者：
Hatano, Naomichi