MATHICSE Technical Report : A fast spectral divide-and-conquer method for banded matrices

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.


Year:
Jan 16 2018
Publisher:
Écublens, MATHICSE
Note:
MATHICSE Technical Report Nr. 01.2018
Laboratories:




 Record created 2019-09-27, last modified 2019-12-05

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