A fast spectral divide-and-conquer method for banded matrices

DOI10.1002/NLA.2365arXiv1801.04175MaRDI QIDQ6296382

Publication date: 12 January 2018

Abstract: Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3): A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix. For this purpose, we combine our previous work on the fast computation of spectral projectors in the so called HODLR format, with a novel technique for extracting a basis for the range of such a HODLR matrix. The numerical experiments demonstrate that our algorithm exhibits quasilinear complexity and allows for conveniently dealing with large-scale matrices.

Mathematics Subject Classification ID

Factorization of matrices (15A23) Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

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