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Submatrix Constrained Inverse Eigenvalue Problem involving Generalised Centrohermitian Matrices in Vibrating Structural Model Correction

Part of: Basic linear algebra Numerical linear algebra

Published online by Cambridge University Press:  27 January 2016

Wei-Ru Xu  and
Guo-Liang Chen
Wei-Ru Xu
Affiliation:
Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200241, P. R. China
Guo-Liang Chen*
Affiliation:
Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200241, P. R. China
*
*Corresponding author. Email addresses:weiruxu@foxmail.com (W.-R. Xu), glchen@math.ecnu.edu.cn (G.-L. Chen)
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Abstract

Generalised centrohermitian and skew-centrohermitian matrices arise in a variety of applications in different fields. Based on the vibrating structure equation where M, D, G, K are given matrices with appropriate sizes and x is a column vector, we design a new vibrating structure mode. This mode can be discretised as the left and right inverse eigenvalue problem of a certain structured matrix. When the structured matrix is generalised centrohermitian, we discuss its left and right inverse eigenvalue problem with a submatrix constraint, and then get necessary and sufficient conditions such that the problem is solvable. A general representation of the solutions is presented, and an analytical expression for the solution of the optimal approximation problem in the Frobenius norm is obtained. Finally, the corresponding algorithm to compute the unique optimal approximate solution is presented, and we provide an illustrative numerical example.

Keywords

Left and right inverse eigenvalue problemoptimal approximation problemgeneralised centrohermitian matrixsubmatrix constraint

MSC classification

Secondary: 65F18: Inverse eigenvalue problems 15A18: Eigenvalues, singular values, and eigenvectors 15A12: Conditioning of matrices
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 1 , February 2016 , pp. 42 - 59
Copyright
Copyright © Global-Science Press 2016 

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