Left and right inverse eigenpairs problem with a submatrix constraint for the generalized centrosymmetric matrix-Reference-Cited by-同舟云学术

Left and right inverse eigenpairs problem with a submatrix constraint for the generalized centrosymmetric matrix

Published:2020-01-01 Issue:1 Volume:18 Page:603-615
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Li Fan-Liang¹²

Affiliation:

1. Institute of Mathematics and Physics , School of Sciences , Central South University of Forestry and Technology , Changsha , 410004 , P. R. China

2. School of Mathematics and Statistics , Changsha University of Science and Technology , Changsha , 410114, Hunan , P. R. China

Abstract

Abstract Left and right inverse eigenpairs problem is a special inverse eigenvalue problem. There are many meaningful results about this problem. However, few authors have considered the left and right inverse eigenpairs problem with a submatrix constraint. In this article, we will consider the left and right inverse eigenpairs problem with the leading principal submatrix constraint for the generalized centrosymmetric matrix and its optimal approximation problem. Combining the special properties of left and right eigenpairs and the generalized singular value decomposition, we derive the solvability conditions of the problem and its general solutions. With the invariance of the Frobenius norm under orthogonal transformations, we obtain the unique solution of optimal approximation problem. We present an algorithm and numerical experiment to give the optimal approximation solution. Our results extend and unify many results for left and right inverse eigenpairs problem and the inverse eigenvalue problem of centrosymmetric matrices with a submatrix constraint.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0020/pdf

Reference27 articles.

1. J. H. Wilkinson, The Algebraic Problem, Oxford University Press, Oxford, 1965.

2. M. Arav, D. Hershkowitz, V. Mehrmann, and H. Schneider, The recursive inverse eigenvalue problem, SIAM J. Matrix Anal. Appl. 22 (2000), no. 2, 392–412, 10.1137/s0895479899354044.

3. R. Loewy and V. Mehrmann, A note on the symmetric recursive inverse eigenvalue problem, SIAM J. Matrix Anal. Appl. 25 (2003), no. 1, 180–187, 10.1137/s0895479802408839.

4. F. L. Li, X. Y. Hu, and L. Zhang, Left and right eigenpairs problem of skew-centrosymmetric matrices, Appl. Math. Comput. 177 (2006), no. 1, 105–110, 10.1016/j.amc.2005.10.035.

5. F. L. Li, X. Y. Hu, and L. Zhang, Left and right inverse eigenpairs problem for κ-persymmetric matrices, Math. Numer. Sin. 29 (2007), no. 4, 337–344.