文章基本信息

标题：Finding The Closest Persymmetric And Skew-Symmetric Matrices.
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作者：María G. Eberle ; María C. Maciel
期刊名称：Mecánica Computacional
印刷版ISSN：2591-3522
出版年度：2007
页码：1789-1802
语种：English
出版社：CIMEC-INTEC-CONICET-UNL
摘要：The class of Procrustes problems has many application in the biological, physical and social sciences just as in the investigation of elastic structures. The problem consists of solving a constrained linear least squares problem defined on a set of the space of matrices . 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. Raydán has studied the rectangular case and minimizing on a feasible set which is an intersection of convex sets of matrices. The method used is based on the alternate projection method. The Toeplitz cases has been analyzed by these authors. In this contribution, the theory and algorithm developed by Higham for the symmetric Procrustes problem are extended to the persymmetric and skew-symmetric cases. The singular value decomposition is used to analyze the problems and to characterized their solutions. Numerical difficulties are discussed and illustrated by examples.
其他摘要：The class of Procrustes problems has many application in the biological, physical and social sciences just as in the investigation of elastic structures. The problem consists of solving a constrained linear least squares problem defined on a set of the space of matrices . 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. Raydán has studied the rectangular case and minimizing on a feasible set which is an intersection of convex sets of matrices. The method used is based on the alternate projection method. The Toeplitz cases has been analyzed by these authors. In this contribution, the theory and algorithm developed by Higham for the symmetric Procrustes problem are extended to the persymmetric and skew-symmetric cases. The singular value decomposition is used to analyze the problems and to characterized their solutions. Numerical difficulties are discussed and illustrated by examples.