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Conditioning Theory for Generalized Inverse C A ‡ and Their Estimations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mahvish Samar & Xinzhong Zhu & Abdul Shakoor, 2023. "Conditioning Theory for Generalized Inverse C A ‡ and Their Estimations," Mathematics, MDPI, vol. 11(9), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2111-:d:1136237
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