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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Least-squares approximation by elements from matrix orbits achieved by gradient flows on compact lie groups
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by Chi-Kwong Li, Yiu-Tung Poon and Thomas Schulte-Herbrüggen PDF
Math. Comp. 80 (2011), 1601-1621 Request permission

Abstract:

Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix $A_0$ by the sum of matrices in $S(A_1), \dots , S(A_N)$ in the sense of finding the Euclidean least-squares distance \[ \min \Big \{\big \|X_1+ \cdots + X_N - A_0\big \|: X_j \in S(A_j), \ j = 1, \dots , N\Big \}.\] Connections of the results to different pure and applied areas are discussed.
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Additional Information
  • Chi-Kwong Li
  • Affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187
  • MR Author ID: 214513
  • Email: ckli@math.wm.edu
  • Yiu-Tung Poon
  • Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50051
  • MR Author ID: 141040
  • Email: ytpoon@iastate.edu
  • Thomas Schulte-Herbrüggen
  • Affiliation: Department of Chemistry, Technical University of Munich, D-85747, Garching, Germany.
  • Email: tosh@ch.tum.de
  • Received by editor(s): September 15, 2008
  • Received by editor(s) in revised form: May 20, 2010
  • Published electronically: December 13, 2010
  • Additional Notes: The author is an honorary professor of the University of Hong Kong and an honorary professor of the Taiyuan University of Technology. His research was partially supported by USA NSF and the William and Mary Plumeri Award.
    The second author’s research was partially supported by USA NSF
    The third author is supported in part by the EU-programmes QAP, Q-ESSENCE and the exchange with COQUIT as well as by the excellence network of Bavaria through QCCC
  • © Copyright 2010 American Mathematical Society
  • Journal: Math. Comp. 80 (2011), 1601-1621
  • MSC (2010): Primary 15A18, 15A60, 15A90; Secondary 37N30
  • DOI: https://doi.org/10.1090/S0025-5718-2010-02450-0
  • MathSciNet review: 2785470