Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE PERIODIC JACOBI MATRIX PROCRUSTES PROBLEM

  • Received : 2009.10.31
  • Accepted : 2009.12.10
  • Published : 2010.05.30
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Abstract

The following "Periodic Jacobi Procrustes" problem is studied: find the Periodic Jacobi matrix X which minimizes the Frobenius (or Euclidean) norm of AX - B, with A and B as given rectangular matrices. The class of Procrustes problems has many application in the biological, physical and social sciences just as in the investigation of elastic structures. The different problems are obtained varying the structure of the matrices belonging to the feasible set. Higham has solved the orthogonal, the symmetric and the positive definite cases. Andersson and Elfving have studied the symmetric positive semidefinite case and the (symmetric) elementwise nonnegative case. In this contribution, we extend and develop these research, however, in a relatively simple way. Numerical difficulties are discussed and illustrated by examples.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

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