Left and right inverse eigenpairs problem of generalized centrosymmetric matrices and its optimal approximation problem. (English) Zbl 1181.65057

Earlier the authors [Appl. Math. Comput. 177, 105–110 (2006; Zbl 1098.65039)] obtained some results for a certain inverse eigenproblem, and an associated approximation problem, for skew-centrosymmetric matrices. This paper gives similar results for the corresponding problem for matrices \(A\) satisfying \(A=KAK\), where \(K\) is a given permutation matrix. For some related results, see the authors [Math. Numer. Sin. 29, No. 4, 337–344 (2007; Zbl 1143.65334)].


65F18 Numerical solutions to inverse eigenvalue problems
Full Text: DOI


[1] Wilkinson, J. H., The Algebraic Problem (1965), Oxford University Press: Oxford University Press Oxford · Zbl 0258.65037
[2] Arav, M.; Hershkowitz, D.; Mehrmann, V.; Schneider, H., The recursive inverse eigenvalue problem, SIAM J. Matrix Anal. Appl., 22, 392-412 (2000) · Zbl 0978.15013
[3] Li, F. L.; Hu, X. Y.; Zhang, L., Left and right eigenpairs problem of skew-centrosymmetric matrices, Appl. Math. Comput., 177, 105-110 (2006) · Zbl 1098.65039
[4] Loewy, R.; Mehrmann, V., A note on the symmetric recursive inverse eigenvalue problem, SIAM J. Matrix Anal. Appl., 25, 180-187 (2003) · Zbl 1062.15010
[5] Pressman, I. S., Matrices with multiple symmetry properties: applications of centrohermitian and perhermitian matrices, Linear Algebra Appl., 284, 239-258 (1998) · Zbl 0957.15019
[6] Datta, L.; Morgera, S. D., On the reducibility of centrosymmetric matrices – applications in engineering problems, Circuits Syst. Signal Process, 8, 71-96 (1989) · Zbl 0674.15005
[7] Xu, S. F., On the Jacobi matrix inverse eigenvalue problem with mixed given data, SIAM J. Matrix Anal. Appl., 17, 632-639 (1996) · Zbl 0856.65032
[8] Zhou, F. Z.; Hu, X. Y.; Zhang, L., The solvability conditions for the inverse eigenvalue problems of centro-symmetric matrices, Linear Algebra Appl., 364, 147-160 (2003) · Zbl 1028.15012
[9] Zhang, Z. Z.; Hu, X. Y.; Zhang, L., The solvability conditions for the inverse eigenvalue problems of Hermitian-generalized Hamiltonian matrices, Inverse Problems, 18, 1369-1376 (2002) · Zbl 1014.65030
[10] Peng, Z. Y., The inverse eigenvalue problem for Hermitian anti-reflexive matrices and its approximation, Appl. Math. Comput., 162, 1377-1389 (2005) · Zbl 1065.65057
[11] Trench, W. F., Inverse eigenproblems and associated approximation problems for matrices with generalized symmetry or skew symmetry, Linear Algebra Appl., 380, 199-211 (2004) · Zbl 1087.15013
[12] Peng, J.; Hu, X. Y.; Zhang, L., A kind of inverse eigenvalue problems of Jacobi matrix, Appl. Math. Comput., 175, 1543-1555 (2006) · Zbl 1098.65040
[13] Peng, J.; Hu, X. Y.; Zhang, L., Two inverse eigenvalue problems for a special kind of matrices, Linear Algebra Appl., 416, 336-347 (2006) · Zbl 1097.65053
[14] Golub, G. H.; Van Loan, C. F., Matrix Computations (1983), Johns Hopkins U.P.: Johns Hopkins U.P. Baltimore · Zbl 0559.65011
[15] Zhang, L.; Xie, D. X., A class of inverse eigenvalue problems, Math. Sci. Acta, 13, 1, 94-99 (1993)
[16] Cheney, E., Introduction to Approximation Theory (1966), McGraw-Hill · Zbl 0161.25202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.