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Variations on Arnoldi’s method for computing eigenelements of large unsymmetric matrices. (English) Zbl 0456.65017

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A42 Inequalities involving eigenvalues and eigenvectors
Software:
SRRIT
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References:
[1] Arnoldi, W.E., The principle of minimized iterations in the solution of the matrix eigenvalue problem, (), 17-29 · Zbl 0042.12801
[2] Björck, A.; Elfving, T., Accelerated projection methods for computing pseudo inverse solutions of systems of linear equations, Nordisk tidskr. informationsbehandling (BIT), 19, 145-163, (1979) · Zbl 0409.65022
[3] Daniel, G.W.; Gragg, W.B.; Kaufmann, L.; Stewart, G.W., Reothogonalization and stable algorithms for updating the Gram-Schmidt QR factorization, Math. comp., 30, 772-795, (1976) · Zbl 0345.65021
[4] Golub, G.H.; Underwood, R., The block Lanczos method for computing eigenvalues, (), 361-377 · Zbl 0407.68040
[5] Jennings, A.; Stewart, W.J., Simultaneous iteration for partial eigensolution of real matrices, J. inst. math. appl., 15, 351-361, (1975) · Zbl 0307.65042
[6] Kaniel, S., Estimates for some computational techniques in linear algebra, Math. comp., 20, 95, 369-378, (1966) · Zbl 0156.16202
[7] Krasnoselskii, M.A., Approximate solutions of operator equations, (1972), Wolters-Nordhoof Groningen
[8] Lanczos, C., An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. res. nat. bur. standards, 45, 4, 255-282, (1950)
[9] Lewis, J.G., Algorithms for sparse matrix eigenvalue problems, Ph.D. thesis, (1977), Stanford Univ. Report 77-595
[10] Lorentz, G.G., Approximation of functions, (1966), Holt, Rinehart & Winston New York · Zbl 0153.38901
[11] Paige, C.C., The computation of eigenvalues and eigenvectors of very large sparse matrices, () · Zbl 0275.65011
[12] Paige, C.C., Bidiagonalization of matrices and solution of linear equations, SIAM J. numer. anal., 11, 197-209, (1974) · Zbl 0244.65023
[13] Parlett, B.N., The symmetric eigenvalue problem, (1980), Prentice-Hall Englewood Cliffs, N.J · Zbl 0431.65016
[14] Ruhe, A., Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse matrices, Math. comp., 33, 146, 680-687, (1979) · Zbl 0443.65022
[15] Saad, Y., Calcul de valeurs propres de grandes matrices hermitiennes par des techniques de partitionnement, ()
[16] Y. Saad, On the rates of convergence of the Lanczos and the block Lanczos methods, SIAM J. Numer. Anal., to appear. · Zbl 0456.65016
[17] Saad, Y., Etude de la convergence du procédé d’Arnoldi pour le calcul d’éléments propres de grandes matrices non symetriques, (), 321
[18] Stewart, G.W., Introduction to matrix computations, (1973), Academic New York · Zbl 0302.65021
[19] G.W. Stewart, \scSRRIT, a \scFORTRAN subroutine to calculate the dominant invariant subspace of a real matrix, ACM Trans. Math. Software, to appear.
[20] Wilkinson, J.H., The algebraic eigenvalue problem, (1965), Clarendon Oxford · Zbl 0258.65037
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