Abstract
A heuristic argument and supporting numerical results are given to demonstrate that a block Lanczos procedure can be used to compute simultaneously a few of the algebraically largest and smallest eigenvalues and a corresponding eigenspace of a large, sparse, symmetric matrixA. This block procedure can be used, for example, to compute appropriate parameters for iterative schemes used in solving the equationAx=b. Moreover, if there exists an efficient method for repeatedly solving the equation (A−σI)X=B, this procedure can be used to determine the interior eigenvalues (and corresponding eigenvectors) ofA closest to σ.
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Cullum, J. The simultaneous computation of a few of the algebraically largest and smallest eigenvalues of a large, sparse, symmetric matrix. BIT 18, 265–275 (1978). https://doi.org/10.1007/BF01930896
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DOI: https://doi.org/10.1007/BF01930896