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The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as they proceed indi- ...
In this thesis we address the computation of a spectral decomposition for symmetric
banded matrices. In light of dealing with large-scale matrices, where classical dense
linear algebra routines are not applicable, it is essential to design alternative tech ...
Sinal-processing on graphs has developed into a very active field of research during the last decade. In particular, the number of applications using frames con-structed from graphs, like wavelets on graphs, has substantially increased. To attain scalabili ...
We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of small relative s ...
Signal-processing on graphs has developed into a very active field of research during the last decade. In particular, the number of applications using frames constructed from graphs, like wavelets on graphs, has substantially increased. To attain scalabili ...
Institute of Electrical and Electronics Engineers0
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 with small bandwidth, w ...
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 c ...
We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of small relative s ...