Small Singular Values Can Increase in Lower Precision

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-08-12 DOI:10.1137/23m1557209

Christos Boutsikas, Petros Drineas, Ilse C. F. Ipsen

引用次数: 0

Abstract

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1518-1540, September 2024.
Abstract. We perturb a real matrix [math] of full column rank, and derive lower bounds for the smallest singular values of the perturbed matrix, in terms of normwise absolute perturbations. Our bounds, which extend existing lower-order expressions, demonstrate the potential increase in the smallest singular values and represent a qualitative model for the increase in the small singular values after a matrix has been downcast to a lower arithmetic precision. Numerical experiments confirm the qualitative validity of this model and its ability to predict singular values changes in the presence of decreased arithmetic precision.

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小奇异值可提高较低精度

SIAM 矩阵分析与应用期刊》，第 45 卷，第 3 期，第 1518-1540 页，2024 年 9 月。摘要。我们对一个全列秩的实矩阵[math]进行扰动，并根据规范绝对扰动推导出扰动矩阵最小奇异值的下限。我们的下界扩展了现有的低阶表达式，证明了最小奇异值的潜在增长，并代表了矩阵降维到较低算术精度后小奇异值增长的定性模型。数值实验证实了这一模型的定性有效性及其预测算术精度降低时奇异值变化的能力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.