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Using a low-storage contour-integral eigensolver for nonsymmetric matrices with collocation to compute vibrational
Luca Corneo1, Tucker Carrington1
1Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada.
Abstract:
Collocation is advantageous for computing vibrational spectra because it obviates the need for quadrature. However, to use collocation, one must solve a non-Hermitian matrix eigenvalue problem. Simple, accurate Lanczos algorithms that require storing only a few vectors can be used only for symmetric matrices. Established eigensolvers for nonsymmetric problems require storing (and orthogonalizing) many vectors. For large matrices, they require a lot of memory. We propose a low-storage eigensolver combining the block Sakurai-Sugiura method and the multi-shift quasi-minimal residual linear solver. It requires storing only a few vectors. The method has many of the advantages of the well-known Cullum-Willoughby Lanczos approach for symmetric matrices.
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