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A New Algorithm for Constrained Matrix Least Squares Approximations

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Abstract

This paper considers the problem of approximating a given symmetric matrix by a symmetric matrix with a prescribed spectrum so that the Frobenius norm of the matrix difference is minimized. By the introduction of a variable search direction, a new convergent algorithm for solving the problem is derived, which is guaranteed to be convergent and is capable of achieving a fast rate of convergence. It is shown that the set of fixed points of the proposed algorithm coincides with the set of equilibrium points of the original double bracket equation. A numerical example is presented to demonstrate superior performance of the proposed algorithm over a standard double bracket algorithm.

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia

    Wei-Yong Yan

  2. Department of Systems Engineering, Research School of Information Sciences and Engineering, The Australian National University, Canberra, ACT, 0200, Australia

    John B. Moore

Authors
  1. Wei-Yong Yan
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  2. John B. Moore
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Yan, WY., Moore, J.B. A New Algorithm for Constrained Matrix Least Squares Approximations. Annals of Operations Research 98, 255–269 (2000). https://doi.org/10.1023/A:1019264609237

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  • DOI: https://doi.org/10.1023/A:1019264609237

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