IRBL: An implicitly restarted block-Lanczos method for large-scale Hermitian eigenproblems
Date of Original Version
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 matrix-vector products with A; in particular, factorization of A is not demanded, nor is the solution of linear systems of equations with the matrix A. This, together with a fairly small storage requirement, makes the irbleigs code well suited for large-scale problems. Applications of the irbleigs code to certain generalized eigenvalue problems and to the computation of a few singular values and associated singular vectors are also discussed. Numerous computed examples illustrate the performance of the method and provide comparisons with other available codes.
SIAM Journal on Scientific Computing
Baglama, J., D. Calvetti, and L. Reichel. "IRBL: An implicitly restarted block-Lanczos method for large-scale Hermitian eigenproblems." SIAM Journal on Scientific Computing 24, 5 (2003): 1650-1677. doi:10.1137/S1064827501397949.