Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian
matrix is an important problem in certain applications, and it is a prerequisite of eigensolvers …

The calculation of a segment of eigenvalues and their corresponding eigenvectors of a
Hermitian matrix or matrix pencil has many applications. A new density-matrix-based …

The FEAST method for solving large sparse eigenproblems is equivalent to subspace
iteration with an approximate spectral projector and implicit orthogonalization. This relation …

Let f(z) be an analytic or meromorphic function in the closed unit disk sampled at the n th
roots of unity. Based on these data, how can we approximately evaluate f(z) or f^(m)(z) at a …

In this paper Beyn's algorithm for solving nonlinear eigenvalue problems is given a new
interpretation and a variant is designed in which the required information is extracted via the …

We study Chebyshev filter diagonalization as a tool for the computation of many interior
eigenvalues of very large sparse symmetric matrices. In this technique the subspace …

We discuss the possibility of using multiple shift–invert Lanczos and contour integral based
spectral projection method to compute a relatively large number of eigenvalues of a large …

This paper discusses techniques for computing a few selected eigenvalue–eigenvector
pairs of large and sparse symmetric matrices. A recently developed class of techniques to …

We consider a nonlinear integral eigenvalue problem, which is a reformulation of the
transmission eigenvalue problem arising in the inverse scattering theory. The boundary …

Methods for the solution of sparse eigenvalue problems that are based on spectral
projectors and contour integration have recently attracted more and more attention. Such …