Algorithm 827
- 1 September 2003
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Mathematical Software
- Vol. 29 (3) , 337-348
- https://doi.org/10.1145/838250.838257
Abstract
Irbleigs is a MATLAB program for computing a few eigenvalues and associated eigenvectors of a sparse Hermitian matrix of large order n . The matrix is accessed only through the evaluation of matrix-vector products. Working space of only a few n -vectors is required. The program implements a restarted block-Lanczos method. Judicious choices of acceleration polynomials make it possible to compute approximations of a few of the largest eigenvalues, a few of the smallest eigenvalues, or a few eigenvalues in the vicinity of a user-specified point on the real axis. irbleigs also can be applied to certain large generalized eigenproblems as well as to the computation of a few nearby singular values and associated right and left singular vectors of a large general matrix.Keywords
This publication has 6 references indexed in Scilit:
- IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian EigenproblemsSIAM Journal on Scientific Computing, 2003
- Dealing with linear dependence during the iterations of the restarted block Lanczos methodsNumerical Algorithms, 2000
- Computation of a Few Small Eigenvalues of a Large Matrix with Application to Liquid Crystal ModelingJournal of Computational Physics, 1998
- ARPACK Users' GuidePublished by Society for Industrial & Applied Mathematics (SIAM) ,1998
- Iterative methods for the computation of a few eigenvalues of a large symmetric matrixBIT Numerical Mathematics, 1996
- Implicit Application of Polynomial Filters in a k-Step Arnoldi MethodSIAM Journal on Matrix Analysis and Applications, 1992