Conditioning Theory for Generalized Inverse C A ‡ and Their Estimations

Mahvish Samar (), Xinzhong Zhu and Abdul Shakoor
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Mahvish Samar: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Xinzhong Zhu: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Abdul Shakoor: Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

Mathematics, 2023, vol. 11, issue 9, 1-19

Abstract: The conditioning theory of the generalized inverse C A ‡ is considered in this article. First, we introduce three kinds of condition numbers for the generalized inverse C A ‡ , i.e., normwise, mixed and componentwise ones, and present their explicit expressions. Then, using the intermediate result, which is the derivative of C A ‡ , we can recover the explicit condition number expressions for the solution of the equality constrained indefinite least squares problem. Furthermore, using the augment system, we investigate the componentwise perturbation analysis of the solution and residual of the equality constrained indefinite least squares problem. To estimate these condition numbers with high reliability, we choose the probabilistic spectral norm estimator to devise the first algorithm and the small-sample statistical condition estimation method for the other two algorithms. In the end, the numerical examples illuminate the obtained results.

Keywords: generalized inverse C A ‡; normwise condition number; mixed and componentwise condition numbers; EILS problem; probabilistic spectral norm estimator; small-sample statistical condition estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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