Implementation Aspects of Band Lanczos Algorithms for Computation of Eigenvalues of Large Sparse Symmetric Matrices
نویسنده
چکیده
A band Lanczos algorithm for the iterative computation of eigenvalues and eigenvectors of a large sparse symmetric matrix is described and tested on numerical examples. It starts with a p dimensional subspace, and computes an orthonormal basis for the Krylov spaces of A, generated from this starting subspace, in which A is represented by a 2p + 1 band matrix, whose eigenvalues can be computed. Special emphasis is given to devising an implementation that gives a satisfactory numerical orthogonality, with a simple program and few arithmetic operations.
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