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An Algorithm of Ordered Schur Factorization For Real Nonsymmetric Matrix

Authors: Lokendra K. Balyan

Abstract:

In this paper, we present an algorithm for computing a Schur factorization of a real nonsymmetric matrix with ordered diagonal blocks such that upper left blocks contains the largest magnitude eigenvalues. Especially in case of multiple eigenvalues, when matrix is non diagonalizable, we construct an invariant subspaces with few additional tricks which are heuristic and numerical results shows the stability and accuracy of the algorithm.

Keywords: Schur Factorization, Eigenvalues of nonsymmetric matrix, Orthoganal matrix.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075270

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References:


[1] Z. Bai, J.W. Demmel, On swapping diagonal blocks in real Schur form, Lin. Alg. appli., Vol. 186, P. 73-95, 1993.
[2] P.V. Dooren, A generalized eigenvalue approch for solving Riccati equations, SIAM Sci. and Stat. Comp, Vol. 2, P. 121-135, 1981.
[3] D.L. Harrer, A block Arnoldi method for large nonsymmetric eigenvalue problem, Centre for Mathematics and its applications, School of Mathematical Science, Australian National University, Canberra, ACT 0200.
[4] Z. Bai, J Demmel, J. Dongarra, A. Ruhe, H. Vorst, Templates for the solustion of algebraic eigenvalue problems, A practical guide, SIAM, Philadelphia, (2000).
[5] J.J. Du Croz, S.J. Hamnarling, Eigenvalue Problems, in Numerical algorithm, Oxford Uni. Press, Newyork, P. 29-66.
[6] G.H. Golub and F. Van Loan, Matrix Computations (3rd Edition) Jhons Hopkins Uni. Press, Baltimore 1996.
[7] B.S. Garbow, J.M. Boyle, J.J. Dongarra, C.B. Moler, Matrix Eigensystem Routines - EISPACK Guide Extension, Lecture Notes in Computer Science, Springer-Verlag, Vol. 51, 1977.
[8] E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. Mckenney, D. Sorensen, LAPACK User-s Guide. SIAM, Philadelphia, 3rd Edition, 1999.