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,453552, India

来源：

Electronic Transactions on Numerical Analysis | 2024年 / 60卷

关键词：

Matrix algebra - Perturbation techniques;

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

共 50 条

[31] A class of modified DPSS preconditioners for generalized saddle-point linear systems
Zhao-Zheng Liang
Guo-Feng Zhang
Computational and Applied Mathematics, 2019, 38
[32] A class of modified DPSS preconditioners for generalized saddle-point linear systems
Liang, Zhao-Zheng
Zhang, Guo-Feng
COMPUTATIONAL & APPLIED MATHEMATICS, 2019, 38 (02):
[33] On the Generalized Shift-HSS Splitting Methods for Nonsingular Saddle Point Problem
Huang, Zhuo-hong
Su, Hong
INTERNATIONAL CONFERENCE ON MECHANICAL, ELECTRONIC AND INFORMATION TECHNOLOGY (ICMEIT 2018), 2018, : 471 - 474
[34] AN ALGORITHM FOR THE SOLUTION OF A GENERALIZED PROBLEM ON LINEAR PROGRAMMING
ZUKHOVITSKII, SI
DOKLADY AKADEMII NAUK SSSR, 1960, 133 (01): : 20 - 23
[35] GENERALIZED SADDLE-POINT CONDITION FOR IGNITION IN A TOKAMAK REACTOR WITH TEMPERATURE AND DENSITY PROFILES
MITARAI, O
HIROSE, A
SKARSGARD, HM
FUSION TECHNOLOGY, 1989, 16 (02): : 197 - 210
[36] ON A GENERALIZED SOLUTION TO A TORSION PROBLEM IN LINEAR ELASTICITY
BRANDT, HE
JOURNAL OF THE AEROSPACE SCIENCES, 1961, 28 (05): : 422 - 424
[37] A Generalized Primal-Dual Algorithm with Improved Convergence Condition for Saddle Point Problems
He, Bingsheng
Ma, Feng
Xu, Shengjie
Yuan, Xiaoming
SIAM JOURNAL ON IMAGING SCIENCES, 2022, 15 (03): : 1157 - 1183
[38] A Generalized KKM Theorem and its Applications to Saddle Point and Nash Equilibrium Problem
Lu, Haishu
PROCEEDINGS OF THE FIRST INTERNATIONAL WORKSHOP ON EDUCATION TECHNOLOGY AND COMPUTER SCIENCE, VOL I, 2009, : 320 - 323
[39] The Analysis of the Augmented Lagrangian Method for Symmetric Saddle Point Problem by Generalized SVD
Okulicka-Dluzewska, Felicja
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017), 2018, 1978
[40] Spectral analysis of the generalized shift-splitting preconditioned saddle point problem
Ren, Zhi-Ru
Cao, Yang
Niu, Qiang
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 311 : 539 - 550

← 1 2 3 4 5 →