Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices
Ho, Diem ; Chatelin, Françoise ; Bennani, Maria
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 24 (1990), p. 53-65 / Harvested from Numdam
Publié le : 1990-01-01
@article{M2AN_1990__24_1_53_0,
     author = {Ho, Diem and Chatelin, Fran\c coise and Bennani, Maria},
     title = {Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {24},
     year = {1990},
     pages = {53-65},
     mrnumber = {1034898},
     zbl = {0695.65020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1990__24_1_53_0}
}
Ho, Diem; Chatelin, Françoise; Bennani, Maria. Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 24 (1990) pp. 53-65. http://gdmltest.u-ga.fr/item/M2AN_1990__24_1_53_0/

[1] F. Chatelin, Valeurs Propres de Matrices, Masson, Paris, 1988. | MR 934203 | Zbl 0691.65018

[2] M. Clint andA. Jennings, The Evaluation of Eigenvalues and Eigenvectors of Real Symmetric Matrices by Simultaneous Iteration Method, J. Inst. Math. Appl., 8, 111-121, 1971. | MR 297116 | Zbl 0221.65070

[3] J. Cullum andR. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1, Theory, Vol. 2, Programs, Birkhauser, Basel, 1985. | Zbl 0574.65028

[4] J. Cullum andR. A. Willoughby, A Practical Procedure for Computing Eigenvalues of large Sparse Nonsymmetric Matrices, in Large Scale Eigenvalue Problems, eds. J. Cullum and R. A. Willoughby, Elsevier Science Publishers B. V. (North-Holland), 1986. | MR 875435 | Zbl 0605.65027

[5] D. Ho, Tchebychev Iteration and Its Optimal Ellipse for Nonsymmetric Matrices, Tech. Rep. F-125, IBM Scientific Center, Paris, 1987.

[6] A. Jennings, Eigenvalue Methods and the Analysis of Structural Vibration, in Sparse Matrices and Their Uses, ed. I. S. Duff, Academic Press, New York, 109-139, 1981. | Zbl 0457.73072

[7] A. Jennings andW. J. Stewart, Simultaneous Iteration for Partial Eigensolution of Real Matrices, J. Math. Inst. Appl., 15, 351-361, 1980. | MR 408221 | Zbl 0307.65042

[8] T. A. Manteuffel, An Iterative Method for Solving Nonsymmetric Linear Systems with Dynamic Estimation of Parameters, Ph. D. dissertation, Tech. Rep. UIUCDCS-75-758, University of Illinois, Urbana-Champaign, 1975.

[9] T. A. Manteuffel, The Tchebychev Iteration for Nonsymmetric Linear Systems, Numer. Math., 28, 307-327, 1977. | MR 474739 | Zbl 0361.65024

[10] T. A. Manteuffel, Adaptive procedure for Estimation of Parameter for the Non-symmetric Tchebychev Iteration, Numer. Math., 31, 183-208, 1978. | MR 509674 | Zbl 0413.65032

[11] B. Nour-Omid,B. N. Parlett andR. Taylor, Lanczos Versus Subspace Iteration for the Solution of Eigenvalue Problems, Int. J. Num. Meth. Engr., 19, 859-871, 1983. | Zbl 0521.65024

[12] B. N. Parlett,D. R. Taylor andZ. Z. Liu, The look ahead Lanczos algorithm for large nonsymmetric eigenproblems, in Computing methods in applied sciences and engineering, eds. R. Glowinski and J. L. Lions, North Holland, 1985. | MR 806772 | Zbl 0564.65021

[13] Y. Saad, Variations on Arnoldi's Method for Computing Eigenelements of Large Unsymmetric Matrices, Linear Algebra Appl., 34, 269-295, 1980. | MR 591435 | Zbl 0456.65017

[14] Y. Saad, Least Squares Polynomials in the Complex Plane with Applications to Solving Sparse Nonsymmetric Matrix Problems, Res. Rep. YALEU/DCS/RR-276, 1983.

[15] Y. Saad, Tchebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems, Math. Comp., 42, 567-588, 1984. | MR 736453 | Zbl 0539.65013

[16] Y. Saad, Partial Eigensolutions of Large Nonsymmetric Matrices, Res. Rep. YALEU/DCS/RR-397, 1985.

[17] G. W. Stewart, Simultaneous Iteration for Computing Invariant Subspace of non-Hermitian Matrices, Numer. Math., 25, 123-136, 1976. | MR 400677 | Zbl 0328.65025

[18] D. Taylor, Analysis of the Look-Ahead Lanczos Algorithm, Ph. D. Thesis, Tech. Rep., Univ. of California, Berkeley, 1983.