Generalized block lanczos methods for large unsymmetric eigenproblems

Numerische Mathematik

Volumn 80, Issue 2, 1998, Pages 239-266

  Jia, Zhongxiao ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032339596     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050367     Document Type: Article

References (49)

1. Arioli, M., Fassino, C. (1994): Roundoff error analysis of algorithms based on Krylov subspace methods. Technical Report, Cerfacs, Toulouse
2. Arnoldi, W.E. (1951): The principle of minimized iteration in the solution of the matrix eigenvalue problem. Quart. Appl. Math. 9, 17-29
3. Bai, Z., Barrett, R., Day, D., Demmel, J., Dongarra, J. (1996): Test matrix collection (non-hermitian eigenvalue problems). Techical Report, Math. Dept., University of Kentucky
4. Chatelin, F. (1983): Spectral Approximation of Linear Operators. Academic Press, New York
5. Chatelin, F. (1986): Ill-conditioned eigenproblems. In: Cullum, J., Willoughby, R.A., eds., Large Scale Eigenvalue Problem, pp. 267-292
6. Chatelin, F., Godet-Thobie, S. (1991): Stability analysis in aeronautical Industries. In: Durand, M., Dabaghi, F.E., eds., High Performance Computing II, pp. 415-422
7. Chatelin, F. (1993): Eigenvalues of Matrices. Wiley, Chichester
8. Chatelin, F. (1994): Influence of nonnormality on the reliability of iterative methods in linear algebra. ILAS 94, Rotterdam
9. Chatelin, F., Fraysse, V. (1996): Lectures on Finite Precision Computations. SIAM, Philadephia
10. Cheney, E.W. (1966): Introduction to Approximation Theory. McGraw-Hill, New York
11. Cullum, J., Willoughby, W.R. (1986): A practical procedure for computing eigenvalues of large sparse nonsymmetric matrices. In: Cullum, J., Willoughby, R.A., eds., Large Scale Eigenvalue Problem, pp. 199-240
12. Daniel, G.W., Gragg, W.B., Kaufmann, L., Stewart, G.W. (1976): Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization. Math. Comp. 30, 772-795
13. Drkosova, J., Greenbaum, A., Rozloznik, M and Strakes, Z. (1995): Numerical stability of GMRES. BIT 35, 309-330
14. Fischer, B., Freund, R.W. (1991): Chebyshev polynomials are not always optimal. J. Approx. Theory 65, 261-272
15. Golub, G.H., Van Loan, C.F. (1989): Matrix Computations. The Johns Hopkins University Press, 2nd Edition, Baltimore
16. Golub, G.H., Underwood, R.R. (1977): The block Lanczos method for computing eigenvalues. In: Rice, J.R., ed., Mathematical Software 3, pp. 361-377. Academic Press, New York
17. Ho, D. (1990): Tchebychev acceleration technique for large scale nonsymmetric matrices. Numer. Math. 56, 721-734
18. Ho, D., Chatelin, F., Patau, J.C. (1988): Arnoldi-Tchebychev procedure for large non-symmetric matrices. Math. Mod. Numer. Anal. 24, 53-65
19. Jia, Z., Xiong, X. (1990): The convergence of generalized Lanczos methods for solving eigenproblems of large unsymmetric matrices. J. Dalian Univ. of Tech.(in Chinese) 30, 1-7
20. Jia, Z. (1994): Some numerical methods for large unsymmetric eigenproblems. Ph.D. thesis, Math. Dept., University of Bielefeld, Germany
21. Jia, Z. (1995): The convergence of generalized Lanczos methods for large unsymmetric eigenproblems. SIAM J. Matrix Anal. Appl. 16, 843-862
22. Jia, Z. (1995): Arnoldi type algorithms for large unsymmetric multiple eigenproblems. Preprint 95-026, Math. Dept., University of Bielefeld, Germany. J. Comput. Math. (to appear)
23. Jia, Z. (1995): A block incomplete orthogonalization method for large nonsymmetric eigenproblems. BIT 35, 516-539
24. Jia, Z., Elsner, L. (1995): Improving eigenvectors in Arnoldi's method. Preprint 95-077, Math. Dept., University of Bielefeld, Germany
25. Jia, Z. (1997): Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems. Linear Algebra Appl. 259: 1-23
26. Jia, Z. (1998): A class of new projection methods for non-Hermitian matrix eigenproblems. Proceedings of the Third China-Japan Seminar on Numerical Mathematics, Shi, Z., ed., Academic Press, Beijing
27. Jia, Z. (1998): A refined iterative algorithm based on the block Arnoldi process for large unsymmetric eigenproblems. Linear Algebra Appl. 270: 171-189
28. Jia, Z. (1996): Some natures and properties of refined orthogonal projection methods for large eigenproblems. Technical Report, Dept. of Applied Mathematics, Dalian University of Technology, China, submitted
29. Jia, Z. (1997): A theoretical comparison of classical and refined orthogonal projection methods. Technical Report, Dept. of Applied Mathematics, Dalian University of Technology, submitted
30. Jia, Z. (1997): A refined subspace iteration algorithm for large sparse eigenproblems. Technical Report, Dept. of Applied Mathematics, Dalian University of Technology, submitted
31. Kerner, W. (1989): Large-scale complex eigenvalue problems. J. Comp. Phys. 53, 1-85
32. Manteuffel, TA. (1977): The Tchebychev iteration for nonsymmetric linear system. Numer. Math. 28, 307-327
33. O'Leary, D.P. (1980): The block conjugate gradient algorithm and the related methods. Linear Algebra Appl. 29, 293-322
34. Parlett, B.N. (1980): The Symmetric Eigenvalue Problem. Prentice Hall, Englewood Cliffs, NJ
35. Ruhe, A. (1983): The two sided Arnoldi algorithm for nonsymmetric eigenvalue problem. In: Kågström, B., Ruhe, A., eds., Matrix Pencils, Lecture Notes in Mathematics 973, pp. 104-120. Springer, Berlin
36. Ruhe, A. (1984): Rational Krylov sequence method for eigenvalue computation. Linear Algebra Appl. 58, 391-405
37. Ruhe, A. (1994): Rational Krylov algorithms for nonsymmetric eigenvalue problems, II: Matrix pairs. Linear Algebra Appl. 197/198, 283-295
38. Ruhe, A. (1994): The rational Krylov algorithm for nonsymmetric eigenvalue problems, III: Complex shifts for real matrices. BIT 34, 165-176
39. Saad, Y. (1980): Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices. Linear Algebra Appl. 34, 269-295
40. Saad, Y. (1983): Projection methods for solving large sparse eigenvalue problems. In: Kågström, B., Ruhe, A. eds., Matrix Pencils, Lecture Notes in Mathematics 973, pp. 121-144. Springer, Berlin
41. Saad, Y. (1984): Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems. Math. Comp. 42, 567-588
42. Saad, Y. (1980): On the rates of convergence of the Lanczos and the block-Lanczos methods. SIAM J. Numer. Anal. 17, 687-706
43. Saad, Y. (1992): Numerical Methods for Large Eigenvalue Problems. Manchester University Press
44. Sadkane, M. (1993): A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices Numer. Math. 64, 181-194
45. Sadkane, M. (1993): Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems. Numer. Math. 64, 195-212
46. Scott, J. A. (1995): An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices. ACM Trans. Math. Softw. 21, 432-475
47. Sorensen, D.C. (1992): Implicit application of polynomials filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13, 357-385
48. Varga, R.S. (1957): A comparison of the successive overrelaxation method and semiiterative method using Chebyshev polynomials. J. Soc. Indust. Appl. Math. 5, 39-46
49. Wilkinson, J.H. (1965): The Algebraic Eigenvalue Problem. Clarendon Press, Oxford