Abstract
The rank-constrained least square problem seeks the matrix X with an assigned rank p such that the Frobenius norm of AX – B is minimized for some given matrices A and B. This problem reduces to the so-called rank-constrained matrix matching problem when thematrix A is an identity one. It is first shown that the solution to the rank-constrained least square problem can be converted to the solution to the rankconstrained matrix matching problem, and then a complete parametric solution to the rank-constrainedmatrix matching problem is presented. The proposed approach is convenient to use and possesses good numerical reliability since itmainly involves a singular value decomposition. To the best knowledge of the authors, such results are novel in the literature.
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Duan, GR. (2010). Rank-Constrained Matrix Matching and Least Square Problems. In: Analysis and Design of Descriptor Linear Systems. Advances in Mechanics and Mathematics, vol 23. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6397-0_13
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DOI: https://doi.org/10.1007/978-1-4419-6397-0_13
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-6396-3
Online ISBN: 978-1-4419-6397-0
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