Najafi, H. Saberi; Ghazvini, H. A modification on minimum restarting method in the Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix. (English) Zbl 1106.65031 Appl. Math. Comput. 181, No. 2, 1455-1461 (2006). Summary: We intend to modify “min restarting method” presented by H. Saberi Najafi and E. Khaleghi [Appl. Math. 156, No. 1, 59–71 (2004; Zbl 1055.65050)] and develop a new algorithm for finding the eigenvalues of a nonsymmetric matrix on the basis of Arnoldi algorithm. In most of the restarting methods the basic idea is the selection of the best initial eigenvector, but our aim is to improve the initial eigenvectors in each iteration of the restarting method. Numerical tests show the algorithm converges rapidly with high accuracy. Cited in 1 Document MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices Keywords:eigenvalue; Hessenberg matrix; Krylov subspace; numerical examples; min restarting method Citations:Zbl 1055.65050 Software:eigs PDFBibTeX XMLCite \textit{H. S. Najafi} and \textit{H. Ghazvini}, Appl. Math. Comput. 181, No. 2, 1455--1461 (2006; Zbl 1106.65031) Full Text: DOI References: [1] Arnoldi, W. E., The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart. Appl. Math., 9, 17-29 (1951), Mr 13:163e · Zbl 0042.12801 [2] Saad, Y., Numerical Solution of Large Nonsymmetric Eigenvalue Problems (1992), Halsted Press: Halsted Press New York [3] Saad, Y., Iterative Method for Sparse Linear Systems (1996), PWS Publishing Company, A Division of International Thomson Publishing Inc.: PWS Publishing Company, A Division of International Thomson Publishing Inc. USA · Zbl 0858.65029 [4] Saberi Najafi, H.; Khaleghi, E., A new restarting method in the Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix, Appl. Math., 156, 59-71 (2004) · Zbl 1055.65050 [5] H. Saberi Najafi, H. Ghazvini, Weighted restarting method in the Weighted Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix, Appl. Math., in press.; H. Saberi Najafi, H. Ghazvini, Weighted restarting method in the Weighted Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix, Appl. Math., in press. · Zbl 1094.65029 [6] Sorenson, D. C., Implicit application of polynomial filters in a \(K\)-step Arnoldi method, SIAM J. Matrix Appl., 13, 357-385 (1992) · Zbl 0763.65025 [7] Morgan, B., Restarting the Arnoldi method for large nonsymmetric eigenvalue problems, Math. Comput., 1213-1230 (1996) · Zbl 0857.65041 [8] Stathopoulos, A.; Saad, Y.; Wu, K., Dynamic thick restarting of the Daridson and the implicitly restarted Arnoldi algorithm, SIAM J. Sci. Comput., 19, 227-245 (1998) · Zbl 0924.65028 [9] R.B. Lehoucq, Analysis and implementation of an implicitly restarted Arnold iteration. Ph.D. thesis, Department of Computational and Applied Mathematics, Rice University, 1995, TR 95-13.; R.B. Lehoucq, Analysis and implementation of an implicitly restarted Arnold iteration. Ph.D. thesis, Department of Computational and Applied Mathematics, Rice University, 1995, TR 95-13. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.