An Algorithm for Numerical Computation of the Jordan Normal Form of a Complex Matrix

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An Algorithm for Numerical Computation of the Jordan Normal Form of a Complex Matrix

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 6 , Issue 3 (September 1980) table of contents

Pages: 398 - 419

Year of Publication: 1980

ISSN:0098-3500

Authors

Bo Kågström	Institute of Information Processing, University of Umeå, S-901 87 Umeå, Sweden
Axel Ruhe	Institute of Information Processing, University of Umeå, S-901 87 Umeå, Sweden

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 7, Downloads (12 Months): 67, Citation Count: 6

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BEAVERS, JR., A N., AND DENMAN, E.D. A new sirmlarity transformation method for elgenvalues and eigenvectors. To appear in Math. B~osc~.
	2	BEKISHEV, G.A. A method of reducing matrices to the Jordan normal form (Transl.) USSR Comput. Math. Math Phys. 5, 4 (1965), 189-195
	3	Peter A. Businger , Gene H. Golub, Algorithm 358: singular value decomposition of a complex matrix [F1, 4, 5], Communications of the ACM, v.12 n.10, p.564-565, Oct. 1969 [doi>10.1145/363235.363249]
	4	FADDEEV, D.K., KUBLANOVSKAYA, V.N., AND FADDEEVA, V.N. 0 re~enii lineinyh algebrai6eskfla sistem s pryamougolnymi matrlcaml. Tr. Mat Inst. V.A Steklova 96 (1968), 79-92.
	5	GANTMACHER, F.R. The Theory of Matrwes (Transl.) Chelsea, New York, 1959.
	6	Gene H. Golub , James H. Wilkinson, Ill-conditioned eigensystems and the computation of the Jordan canonical form., Stanford University, Stanford, CA, 1975
	7	GREGORY, R.T., AND KARNEY, D.L A Collection of Matrices for Testing Computational Algorithms. Wiley, New York, 1969.
	8	HOUSEHOLDER, A.S. The Theory of Matr~ces in Numerwal Analysts Blaisdell, New York, 1964.
	9	K/~GSTROM, B., AND RUHE, A. The Fortran program for numerical computation of the Jordan normal form of a complex matrLx. Rep. UMINF-51.74, Univ. Ume~, Ume~, Sweden, 1974.
	10	KAHAN, W Conserving confluence curbs ill-condition. Tech. Rep. 6, Dep Comput. Sci., Umv. California, Berkeley, Calif., 1972, pp. 1-54.
	11	KATO, T Perturbatmn Theory for Linear Operators. Sprmger-Verlag, New York, 1966.
	12	KREISSELMEIER, G On the determination of the Jordan form of a matrix. IEEE Trans. Automat. Contr. AC-18 (1973), 686-687.
	13	KUBLANOVSKAYA, V.N On a method of solving the complete elgenvalue problem for a degenerate matrix. Zh. Vychisl. Mat. Mat. F~z. 6 (1966), 611-620; Transl. m USSR Comput Math. Math. Phys. 6, 4 (1968), 1-14.
	14	LANCASTER, P. Lambda-Matr~ces and V~brat~ng Systems. Pergamon Press, London, 1966.
	15	LANCASTER, P. Theory of Matrwes. Academic Press, New York, 1969
	16	RuRIN, W., AND REVINGTON, A. A general method for transforming a matrLx into Jordan canomcal form. Tech. Rep. TR-68-5, Dep. Elec. Eng., Syracuse Univ., Syracuse, N.Y, 1968
	17	RUHE, A. An algorithm for numerical determination of the structure of a general matrix. BIT 10 (1970), 196-216.
	18	RUHE, A Perturbation bounds for means of eigenvalues and invariant subspaces. BIT 10 (1970), 343-354.
	19	SMITH, B.T., ET AL. Matrix Eigensystem Routmes--EISPACK Guide. Springer-Verlag, New York, 1974.
	20	SRIDHAR, B., AND JORDAN, D. An algorithm for calculation of the Jordan canonical form of a matrix. Comput. Electr. Eng 1 (1973), 239-254.
	21	VARAH, J.M. The computation of bounds for the mvariant subspaces of a general matrix operator. Stanford Tech. Rep. CS 66, Stanford Univ., Stanford, Calif., 1967.
	22	VARAH, J.M. The calculation of the elgenvectors of a general complex matrix by inverse iteration. Math. Comp. 22 (1968), 785-791.
	23	VARAH, J.M. Computing invariant subspaces of a general matrix when the eigensystem is poorly condihoned. Math. Comp. 24 (1970), 137-149.
	24	J. H. Wilkinson, The algebraic eigenvalue problem, Oxford University Press, Inc., New York, NY, 1988
	25	WILKINSON, J.H. Note on matrices with a very ill-conditioned eigenproblem. Numer. Math. 19 (1972), 176-178.
	26	WILKINSON, J.H.Inverse iteration m theory and m practice. Syrup Math. 10 (1971/1972), 361- 379
	27	J. H. Wilkinson , C. Rinsch , F. L. Bauer, Handbook for Automatic Computation: Linear Algebra (Grundlehren Der Mathematischen Wissenschaften, Vol 186), SpringerVerlag, 1986

CITED BY 6

	James Demmel , Bo Kågström, The generalized Schur decomposition of an arbitrary pencil A–&lgr;B—robust software with error bounds and applications. Part II: software and applications, ACM Transactions on Mathematical Software (TOMS), v.19 n.2, p.175-201, June 1993
	James Demmel , Bo Kågström, The generalized Schur decomposition of an arbitrary pencil A–&lgr;B—robust software with error bounds and applications. Part I: theory and algorithms, ACM Transactions on Mathematical Software (TOMS), v.19 n.2, p.160-174, June 1993
	Bo Kågström , Axel Ruhe, Algorithm 560: JNF, An Algorithm for Numerical Computation of the Jordan Normal Form of a Complex Matrix [F2], ACM Transactions on Mathematical Software (TOMS), v.6 n.3, p.437-443, Sept. 1980
	Yimin Wei, Perturbation bound of the Drazin inverse, Applied Mathematics and Computation, v.125 n.2-3, p.231-244, 25 January 2002
	A. V. Ramesh , Kishor Trivedi, Semi-numerical transient analysis of Markov models, Proceedings of the 33rd annual on Southeast regional conference, March 17-18, 1995, Clemson, South Carolina
	Tomohiro Suzuki , Toshio Suzuki, An eigenvalue problem for derogatory matrices, Journal of Computational and Applied Mathematics, v.199 n.2, p.245-250, 15 February 2007