J. Baglama
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.
Supplemental Material
Available for Download
Software for "irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix"
- Baglama, J. 2000. Dealing with linear dependence during the iterations of the restarted block Lanczos methods. Numer. Algorithms 25, 23--36.Google Scholar
- Baglama, J., Calvetti, D., and Reichel, L. 1996. Iterative methods for the computation of a few eigenvalues of a large symmetric matrix. BIT 36, 400--421.Google Scholar
- Baglama, J., Calvetti, D., and Reichel, L. 2003. IRBL: An implicitly restarted block Lanczos method for large-scale Hermitian eigenproblems. SIAM J. Sci. Comput. 24, 1650--1677. Google Scholar
- Baglama, J., Calvetti, D., Reichel, L., and Ruttan, A. 1998. Computation of a few small eigenvalues of a large matrix with applications to liquid crystal modeling. J. Comput. Phys. 146, 203--226. Google Scholar
- Calvetti, D., Reichel, L., and Sorensen, D. C. 1994. An implicitly restarted Lanczos method for large symmetric eigenvalue problems. Elec. Trans. Numer. Anal. 2, 1--21.Google Scholar
- Lehoucq, R. B., Sorensen, D. C., and Yang, C. 1998. ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM, Philadelphia, Pa. Code available at web site http://www.caam.rice.edu/software/ARPACK.Google Scholar
- MathWorks. 1998. MATLAB Application Program Interface Guide, Version 5.Google Scholar
- Sorensen, D. C. 1992. Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13, 357--385. Google Scholar
Index Terms
- Algorithm 827: irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix
Recommendations
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
Special issue on the Advanced CompuTational Software (ACTS) CollectionThe Scalable Library for Eigenvalue Problem Computations (SLEPc) is a software library for computing a few eigenvalues and associated eigenvectors of a large sparse matrix or matrix pencil. It has been developed on top of PETSc and enforces the same ...
IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian Eigenproblems
The irbleigs code is an implementation of an implicitly restarted block-Lanczos method for computing a few selected nearby eigenvalues and associated eigenvectors of a large, possibly sparse, Hermitian matrix A. The code requires only the evaluation of ...
Computation of a Few Small Eigenvalues of a Large Matrix with Application to Liquid Crystal Modeling
Equilibrium configurations of liquid crystals in a finite containment are minimizers of the thermodynamic free energy of the system. It is important to be able to track an equilibrium configuration as the temperature of the liquid crystals is decreased. ...
Comments