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A Contribution to Condition Numbers of Quaternion Least Squares Problems

Author

Listed:
  • Qiaohua Liu

    (Shanghai University
    Shanghai University)

  • Yuejuan Yu

    (Shanghai University
    Shanghai University)

  • Yimin Wei

    (Fudan University)

Abstract

This paper investigates the quaternion linear least squares problem and presents the explicit expressions of the normwise, mixed and componentwise condition numbers for the least squares solution and its residuals. Compact and tight upper bounds for these condition numbers are provided. For equilibratory input data, tightness of the normwise condition number and upper bounds are shown in estimating the actual forward errors and the residuals of the solution. For general sparse and badly scaled problems, mixed and componentwise condition numbers are shown to be much tighter than the one based on the normwise condition number.

Suggested Citation

  • Qiaohua Liu & Yuejuan Yu & Yimin Wei, 2025. "A Contribution to Condition Numbers of Quaternion Least Squares Problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(3), pages 989-1004, September.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:3:d:10.1007_s13226-025-00815-4
    DOI: 10.1007/s13226-025-00815-4
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