STRUCTURED CONDITION NUMBERS FOR A LINEAR FUNCTION OF THE SOLUTION OF THE GENERALIZED SADDLE POINT PROBLEM

被引：0

作者：

Ahmad, S.K. Safique ^{[1
]}

Khatun, Pinki ^{[1
]}

机构：

[1] Department of Mathematics, Indian Institute of Technology Indore, Khandwa Road, Madhya Pradesh, Indore

来源：

Electronic Transactions on Numerical Analysis | 2024年 / 60卷

关键词：

condition number; generalized saddle point problems; perturbation analysis; Toeplitz matrices; weighted Toeplitz regularized least-squares problem;

D O I：

10.1553/etna_vol60s471

中图分类号：

学科分类号：

摘要：

This paper addresses structured normwise, mixed, and componentwise condition numbers (CNs) for a linear function of the solution to the generalized saddle point problem (GSPP). We present a general framework that enables us to measure structured CNs of the individual components of the solution. Then, we derive their explicit formulae when the input matrices have symmetric, Toeplitz, or some general linear structures. In addition, compact formulae for unstructured CNs are obtained, which recover previous results on CNs for GSPPs for specific choices of the linear function. Furthermore, applications of the derived structured CNs are provided to determine the structured CNs for the weighted Toeplitz regularized least-squares problems and Tikhonov regularization problems, which recovers some previous studies in the literature. Copyright © 2024, Kent State University.

引用

页码：471 / 500

页数：29

共 22 条

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