Accurate singular values of a class of parameterized negative matrices

被引：0
作者：
Rong Huang
Jungong Xue
机构：
[1] Hunan University of Science and Technology,School of Mathematics and Computational Science
[2] Fudan University,School of Mathematical Science
来源：
Advances in Computational Mathematics | 2021年 / 47卷
关键词：
Negative matrices; Singular values; High relative accuracy; Parametrization; 65F15; 15A18; 15B99;
D O I：
暂无
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学科分类号：
摘要：
Typically, parametrization captures the essence of a class of matrices, and its potential advantage is to make accurate computations possible. But, in general, parametrization suitable for accurate computations is not always easy to find. In this paper, we introduce a parametrization of a class of negative matrices to accurately solve the singular value problem. It is observed that, given a set of parameters, the associated nonsingular negative matrix can be orthogonally transformed into a totally nonnegative matrix in an implicit and subtraction-free way, which implies that such a set of parameters determines singular values of the associated negative matrix accurately. Based on this observation, a new O(n3) algorithm is designed to compute all the singular values, large and small, to high relative accuracy.
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