Abstract
We propose an extension of the Arnoldi-Chebyshev algorithm to the large complex non Hermitian case. We demonstrate the algorithm on two applied problems.
Abstract
Предлагается обобшение алгоритма Арнольди-Небышева для случая болыших комплексных неэрмитовых матрип. Работа алгоритма продемонстрирована на примере двух приклалных задач.
Similar content being viewed by others
References
Chatelin, F., Ho, D., and Bennani, M.Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices. Mathematical Modelling and Numerical Analysis1 (1990), pp. 53–65.
Duff, I. S., Grimes, R. G., and Lewis, J. G.Sparse matrix test problems. ACM Trans. Math. Softw.15 (1989), pp. 1–14.
Fischer, B. and Freund, R.Chebyshev polynomials are not always optimal. J. Approximation Theory65 (1991), pp. 261–273.
Heuveline, V.Polynomial acceleration in the complex plane. Technical report, Irisa/Inria, 1995.
Ho, D.Tchebychev acceleration technique for large scale nonsymmetric matrices. Numer. Math.56 (1990), pp. 721–734.
Kerner, W.Large-scale complex eigenvalue problems. J. Comp. Phys.85 (1989), pp. 1–85.
Manteuffel, T. A.The Tchebychev iteration for nonsymmetric linear system. Numer. Math.28 (1977), pp. 307–327.
Manteuffel, T. A.Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration. Numer. Math.31 (1978), pp. 183–208.
Moler, C. B. and Stewart, G. W.An algorithm for generalized matrix eigenvalue problems. SIAM J. Num. Anal.10 (1973), pp. 241–256.
Rivlin, T. J.The Chebyshev polynomials: from approximation theory to algebra and number theory. J. Wiley and Sons Inc., New-York, 1990.
Saad, Y.Numerical methods for large eigenvalue problems. Algorithms and architectures for advanced scientific computing. Manchester University Press, Manchester, 1992.
Sadkane, M.A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices. Numer. Math.64 (1993), pp. 181–193.
Yamamoto, Y. and Ohtsubo, H.Subspace iteration accelerated by using Chebyshev polynomials for eigenvalue problems with symmetric matrices. Int. J. Numer. Methods Eng.10 (1976), pp. 935–944.
Author information
Authors and Affiliations
Additional information
© V. Heuveline, M. Sadkane, 1996
Rights and permissions
About this article
Cite this article
Heuveline, V., Sadkane, M. Chebyshev acceleration techniques for large complex non hermitian eigenvalue problems. Reliable Comput 2, 111–117 (1996). https://doi.org/10.1007/BF02425912
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02425912