Generalizations of davidson's method for computing eigenvalues of large nonsymmetric matrices

作者: Ronald B Morgan

DOI: 10.1016/0021-9991(92)90006-K

关键词:

摘要: Abstract Davidson's method for nonsymmetric eigenvalue problems is examined. Some analysis given why effective. An implementation that avoids use of complex arithmetic. This reduces the expense if eigenvalues are computed. Also discussed a generalization applies preconditioning techniques developed systems linear equations to problems. Convergence can be rapid there an approximation matrix both factorable and fairly accurate.

参考文章(19)
Ronald B. Morgan, David S. Scott, Generalizations of Davidson’s Method for Computing Eigenvalues of Sparse Symmetric Matrices SIAM Journal on Scientific and Statistical Computing. ,vol. 7, pp. 817- 825 ,(1986) , 10.1137/0907054
K. Hirao, H. Nakatsuji, A generalization of the Davidson's method to large nonsymmetric eigenvalue problems Journal of Computational Physics. ,vol. 45, pp. 246- 254 ,(1982) , 10.1016/0021-9991(82)90119-X
Dianne P. O’Leary, Gene H. Golub, Some History of the Conjugate Gradient and Lanczos Algorithms: 1948–1976 SIAM Review. ,vol. 31, pp. 50- 102 ,(1989) , 10.1137/1031003
J. A. Meijerink, H. A. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix Mathematics of Computation. ,vol. 31, pp. 148- 162 ,(1977) , 10.1090/S0025-5718-1977-0438681-4
Ronald B Morgan, Davidson's method and preconditioning for generalized eigenvalue problems Journal of Computational Physics. ,vol. 89, pp. 241- 245 ,(1990) , 10.1016/0021-9991(90)90124-J
Ronald B. Morgan, David S. Scott, Preconditioning the Lanczos algorithm for sparse symmetric eigenvalue problems SIAM Journal on Scientific Computing. ,vol. 14, pp. 585- 593 ,(1993) , 10.1137/0914037
Lawrence Berkeley Laboratory, Block Preconditioning for the Conjugate Gradient Method SIAM Journal on Scientific and Statistical Computing. ,vol. 6, pp. 220- 252 ,(1985) , 10.1137/0906018
Y. Saad, Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices Linear Algebra and its Applications. ,vol. 34, pp. 269- 295 ,(1980) , 10.1016/0024-3795(80)90169-X