Generalized block anti-Gauss quadrature rules
Generalized block anti-Gauss quadrature rules
复制标题
广义块反高斯求积规则
DOI：
10.1007/s00211-019-01069-z
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发表时间：
2019
影响因子：
2.1
通讯作者：
Reichel, Lothar
中科院分区：
文献类型：
--
作者：
Alqahtani, Hessah;Reichel, Lothar
Golub和Meurant描述了如何应用高斯和高斯-拉多正交规则对确定由对称矩阵定义的实值矩阵泛函的低成本可计算的上界和下界。然而，有许多矩阵泛函，其技术不能保证提供上界和下界。在这种情况下，可以通过计算高斯和反高斯规则对来确定上界和下界。不幸的是，很难确定由高斯规则和反高斯规则确定的值是否包含给定实值矩阵泛函的值。因此，最近描述了反高斯规则的推广，这样，当高斯和（标准）反高斯规则对不能确定实值矩阵泛函的上界和下界时，高斯和广义反高斯规则对也可以确定。可用的推广要求定义泛函的矩阵是实数和对称的。本文回顾了现有的反高斯规则和广义反高斯规则，并对它们进行了扩展，使它们能够在新的情况下应用。特别是，praniki和Reichel （J Comput应用数学284:235-243,2015）中描述的实值非负测度的广义反高斯规则被扩展到允许估计由非对称矩阵定义的矩阵泛函中的误差，以及矩阵值矩阵函数。还描述了给出更简单公式的修改，从而使规则的应用更容易，并适用于更大类的问题。
Golub and Meurant describe how pairs of Gauss and Gauss–Radau quadrature rules can be applied to determine inexpensively computable upper and lower bounds for certain real-valued matrix functionals defined by a symmetric matrix. However, there are many matrix functionals for which their technique is not guaranteed to furnish upper and lower bounds. In this situation, it may be possible to determine upper and lower bounds by evaluating pairs of Gauss and anti-Gauss rules. Unfortunately, it is difficult to ascertain whether the values determined by Gauss and anti-Gauss rules bracket the value of the given real-valued matrix functional. Therefore, generalizations of anti-Gauss rules have recently been described, such that pairs of Gauss and generalized anti-Gauss rules may determine upper and lower bounds for real-valued matrix functionals also when pairs of Gauss and (standard) anti-Gauss rules do not. The available generalization requires the matrix that defines the functional to be real and symmetric. The present paper reviews available anti-Gauss and generalized anti-Gauss rules and extends them in several ways that allow applications in new situations. In particular, the genarlized anti-Gauss rules for a real-valued non-negative measure described in Pranić and Reichel (J Comput Appl Math 284:235–243, 2015) are extended to allow the estimation of the error in matrix functionals defined by a non-symmetric matrix, as well as to matrix-valued matrix functions. Modifications that give simpler formulas and thereby make the application of the rules both easier and applicable to a larger class of problems also are described.
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DOI：
10.1137/s0895479890188803
发表时间：
1994
期刊：
SIAM J. Matrix Anal. Appl.
影响因子：
--
作者：
M. Gutknecht
通讯作者：
M. Gutknecht
DOI：
--
发表时间：
2005
期刊：
--
影响因子：
--
作者：
G. Szabó
通讯作者：
G. Szabó
DOI：
10.1553/etna_vol50s1
发表时间：
2018
期刊：
--
影响因子：
--
作者：
S. Pozza;M. Pranic;Z. Strakoš
通讯作者：
S. Pozza;M. Pranic;Z. Strakoš
影响因子：
1.5
作者：
GUTKNECHT, MH
通讯作者：
GUTKNECHT, MH
DOI：
--
发表时间：
2016
期刊：
影响因子：
--
作者：
S. Pozza;M. Pranic;Z. Strakoš
通讯作者：
Z. Strakoš