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The condition numbers for weighted Moore-Penrose inverse and weighted linear least squares problem
Authors:Shu-fan Wang  Zhi-ping Xiong  Zi-zhen Li
Institution:School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China
Abstract:Condition numbers play an important role in numerical analysis. Classical normise condition numbers are used to measure the size of both input perturbations and output errors. In this paper, we study the weighted normwise relative condition numbers for the weighted Moore-Penrose inverse and the weighted linear least-squares (WLS) problems in the case of the full-column rank matrix. The bounds or formulas for the weighted condition numbers are presented. The obtained results can be viewed as extensions of the earlier works studied by others.
Keywords:Condition number  Weighted linear least squares problem  Weighted Moore-Penrose inverse  Perturbation
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