منابع مشابه
On the squared unsymmetric Lanczos method
The biorthogonal Lanczos and the biconjugate gradient methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld (1989) obtained the conjugate gradient squared by squaring the matrix polynomials of the biconjugate gradient method. Here we square the unsymmetric (or biorthogonal) Lanczos method for computing the eigenvalue...
متن کاملThe Improved Unsymmetric Lanczos Process on Massively Distributed Memory Computers
|For the eigenvalues of a large and sparse unsym-metric coeecient matrix, we propose an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. Stability is obtained by a coupled two-term recurrences procedure that generates Lanczos vectors scaled to unit length. The algorithm is derived such that all inner products and matrix...
متن کاملA Refined Unsymmetric Lanczos Eigensolver for Computing Accurate Eigentriplets of a Real Unsymmetric Matrix
For most unsymmetric matrices it is difficult to compute many accurate eigenvalues using the primitive form of the unsymmetric Lanczos algorithm (ULA). In this paper we propose a modification of the ULA. It is related to ideas used in [J. Chem. Phys. 122 (2005), 244107 (11 pages)] to compute resonance lifetimes. Using the refined ULA we suggest, the calculation of accurate extremal and interior...
متن کاملGeneralized block Lanczos methods for large unsymmetric eigenproblems
Generalized block Lanczos methods for large unsymmetric eigenproblems are presented, which contain the block Arnoldi method, and the block Arnoldi algorithms are developed. The convergence of this class of methods is analyzed when the matrix A is diagonalizable. Upper bounds for the distances between normalized eigenvectors and a block Krylov subspace are derived, and a priori theoretical error...
متن کاملEfficient Implementation of the Improved Unsymmetric Lanczos Process on Massively Distributed Memory Computers
For the eigenvalues of a large and sparse unsymmetric co-eecient matrix, we have proposed an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. The algorithm is derived such that all inner products and matrix-vector multiplications of a single iteration step are independent and communication time required for inner produc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1994
ISSN: 0377-0427
DOI: 10.1016/0377-0427(94)90395-6