Backward errors for eigenproblem of two kinds of structured matrices

In this paper, we consider backward errors in the eigenproblem of symmetric centrosymmetric and symmetric skew-centrosymmetric matrices. By making use of the properties of symmetric centrosymmetric and symmetric skew-centrosymmetric matrices, we derive explicit formulae for the backward errors of approximate eigenpairs.

[1]  Qiang Ye,et al.  ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems , 1999, SIAM J. Matrix Anal. Appl..

[2]  O. Rojo,et al.  Some results on symmetric circulant matrices and on symmetric centrosymmetric matrices , 2004 .

[3]  Zhaojun Bai,et al.  Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem , 1994 .

[4]  Françoise Tisseur,et al.  A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems , 2002, SIAM J. Matrix Anal. Appl..

[5]  D. Xie,et al.  Theory and method for updating least-squares finite element model of symmetric generalized centro-symmetric matrices , 2008 .

[6]  Georg Heinig,et al.  Fast Algorithms for Centro-Symmetric and Centro-Skewsymmetric Toeplitz-Plus-Hankel Matrices , 2004, Numerical Algorithms.

[7]  Mao-lin Liang,et al.  An efficient algorithm for the generalized centro-symmetric solution of matrix equation A X B = C , 2007, Numerical Algorithms.

[8]  Alan L. Andrew.  Classroom Note: Centrosymmetric Matrices , 1998, SIAM Rev..

[9]  I. J. Good,et al.  The Inverse of a Centrosymmetric Matrix , 1970 .

[10]  W. D. Ray.  The Inverse of a Finite Toeplitz Matrix , 1970 .

[11]  Ren-Cang Li.  Relative perturbation theory. III. More bounds on eigenvalue variation , 1997 .

[12]  Ren-Cang Li.  Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations , 1998, SIAM J. Matrix Anal. Appl..

[13]  T. L. Boullion,et al.  The pseudoinverse of a centrosymmetric matrix , 1973 .

[14]  Chuanqing Gu,et al.  The iterative methods for centrosymmetric matrices , 2007, Appl. Math. Comput..

[15]  Volker Mehrmann,et al.  A Chart of Numerical Methods for Structured Eigenvalue Problems , 1992, SIAM J. Matrix Anal. Appl..

[16]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .