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Approximation of Matrices and a Family of Gander Methods for Polar Decomposition

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Abstract

Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank approximants. Properties of Gander methods are investigated in details.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    B. Laszkiewicz & K. Ziętak

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  1. B. Laszkiewicz
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  2. K. Ziętak
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Correspondence to B. Laszkiewicz or K. Ziętak.

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AMS subject classification (2000)

65F30, 15A18

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Laszkiewicz, B., Ziętak, K. Approximation of Matrices and a Family of Gander Methods for Polar Decomposition. Bit Numer Math 46, 345–366 (2006). https://doi.org/10.1007/s10543-006-0053-4

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