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Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices. (English) Zbl 0328.65025

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A18 Eigenvalues, singular values, and eigenvectors
Software:
EISPACK
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References:
[1] Bauer, F. L.: Das Verfahren der Treppeniteration und verwandte Verfahren zur L?sung algebraischer Eigenwertprobleme. Z. Angew. Math. Phys.8, 214-235 (1957) · Zbl 0078.12103 · doi:10.1007/BF01600502
[2] Clint, M., Jennings, A.: The evaluation of eigenvalues and eigenvectors of real symmetric matrices by simultaneous iteration. Comp. J.13, 76-80 (1970) · Zbl 0194.18203 · doi:10.1093/comjnl/13.1.76
[3] Clint, M., Jennings, A.: A simultaneous iteration method for the unsymmetric eigenvalue problem, J. Inst. Math. Appl.8, 111-121 (1971) · Zbl 0221.65070 · doi:10.1093/imamat/8.1.111
[4] Jennings, A.: A direct iteration method of obtaining latent roots and vectors of a symmetric matrix. Proc. Cambridge Philos. Soc.63, 755-765 (1967) · Zbl 0228.65029 · doi:10.1017/S030500410004175X
[5] Parlett, B. N., Poole, W. G.: A geometric theory for the QR, LU, and power iterations, SIAM J. Numer. Anal.10, 389-412 (1973) · Zbl 0253.65018 · doi:10.1137/0710035
[6] Rutishauser, H.: Computational aspects of F. L. Bauer’s simultaneous iteration method, Numer. Math.13, 4-13 (1969) · Zbl 0182.21304 · doi:10.1007/BF02165269
[7] Rutishauser, H.: Simultaneous iteration method for symmetric matrices. Numer. Math.16, 205-223 (1970) · Zbl 0239.65037 · doi:10.1007/BF02219773
[8] Smith, B. T., Boyle, J. M., Garbow, B. S., Ikebe, Y., Klema, V. C., Moler, C. B.: Lecture Notes in Computer Science V6: Matrix Eigensystem Routines-EISPACK Guide. New York: Springer 1974
[9] Stewart, G. W.: Accelerating the orthogonal iteration for the eigenvectors of a Hermitian matrix. Numer. Math.13, 362-376 (1969) · Zbl 0185.40203 · doi:10.1007/BF02165413
[10] Stewart, G. W.: Error bounds for approximate invariant subspaces of closed linear operators. SIAM J. Numer. Anal.8, 796-808 (1971) · Zbl 0232.47010 · doi:10.1137/0708073
[11] Stewart, G. W.: Introduction to Matrix Computations. New York: Academic Press 1973 · Zbl 0302.65021
[12] Stewart, G. W.: Methods of simultaneous iteration for calculating eigenvectors of matrices. In: Topics in Numerical Analysis II (John J. H. Miller, ed.). New York: Academic Press 1975, pp. 185-189 · Zbl 0353.65020
[13] Stewart, G. W.: Perturbation bounds for the QR factorization of a matrix. University of Maryland Computer Science Department Technical Report TR-323 (1974). To appear in SIAM F. Numer. Anali
[14] Vandergraft, J. S.: Generalized Rayleigh methods with applications to finding eigenvalues of large matrices. Lin. Alg. and Appl. (1971) p. 353-368 · Zbl 0222.65047
[15] Wilkinson, J. H., Reinsch, C. (eds.): Handbook for Automatic Computation VII Linear Algebra. New York: Springer 1971 · Zbl 0219.65001
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