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IRBL: An implicitly restarted block-lanczos method for large-scale Hermitian eigenproblems
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DOI：10.1137/S1064827501397949.png)
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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.
Keyword:
block-Lanczos method
eigenvalue computation
singular value computation
polynomial acceleration
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