On condition numbers for Moore–Penrose inverse and linear least squares problem involving Kronecker products |
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| Authors: | Huaian Diao Weiguo Wang Yimin Wei Sanzheng Qiao |
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| Affiliation: | 1. School of Mathematics and Statistics, Key Laboratory for Applied Statistics of MOE, Northeast Normal University, , Chang Chun 130024, China;2. School of Mathematical Sciences, Ocean University of China, , Qingdao, 266100 China;3. School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, , Shanghai, 200433 China;4. Department of Computing and Software, McMaster University, , Hamilton, Ontario L8S 4K1, Canada |
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| Abstract: | In this paper, we investigate the normwise, mixed, and componentwise condition numbers and their upper bounds for the Moore–Penrose inverse of the Kronecker product and more general matrix function compositions involving Kronecker products. We also present the condition numbers and their upper bounds for the associated Kronecker product linear least squares solution with full column rank. In practice, the derived upper bounds for the mixed and componentwise condition numbers for Kronecker product linear least squares solution can be efficiently estimated using the Hager–Higham Algorithm. Copyright © 2012 John Wiley & Sons, Ltd. |
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| Keywords: | condition number Kronecker product linear least squares Moore– Penrose inverse normwise mixed componentwise perturbation |
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