Usually one avoids numerical algorithms involving operations with large, fully populated
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …

This paper presents an efficient method to perform structured matrix approximation by
separation and hierarchy (SMASH), when the original dense matrix is associated with a …

For dense symmetric matrices with small off-diagonal (numerical) ranks and in a
hierarchically semiseparable form, we give a divide-and-conquer eigendecomposition …

In this paper, we propose a structured bisection method with adaptive randomized sampling
for finding selected or all of the eigenvalues of certain real symmetric matrices A. For A with …

We present a superfast divide-and-conquer method for finding all the eigenvalues as well as
all the eigenvectors (in a structured form) of a class of symmetric matrices with off-diagonal …

Matrices with low-rank off-diagonal blocks are a versatile tool to perform matrix compression
and to speed up various matrix operations, such as the solution of linear systems. Often, the …

We consider the approximate computation of spectral projectors for symmetric banded
matrices. While this problem has received considerable attention, especially in the context of …

We consider computing the k-th eigenvalue and its corresponding eigenvector of a
generalized Hermitian eigenvalue problem of n× n large sparse matrices. In electronic …

Hierarchical low-rank approximation of dense matrices can reduce the complexity of their
factorization from O (N 3) to O (N). However, the complex structure of such hierarchical …

We present a fast contour-integral eigensolver for finding selected or all of the eigenpairs of
a non-Hermitian matrix based on a series of analytical and computational techniques, such …