A Contribution to Condition Numbers of Quaternion Least Squares Problems

Qiaohua Liu (), Yuejuan Yu () and Yimin Wei ()
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Qiaohua Liu: Shanghai University
Yuejuan Yu: Shanghai University
Yimin Wei: Fudan University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 989-1004

Abstract: 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.

Keywords: Quaternion least squares problem; Multiple right-hand sides; Normwise condition number; Mixed condition number; Componentwise condition number; 15A12; 65F35 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00815-4

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