It is well known that the trapezoidal rule converges geometrically when applied to analytic
functions on periodic intervals or the real line. The mathematics and history of this …

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 Sakurai–Sugiura projection method, which solves generalized eigenvalue problems to
find certain eigenvalues in a given domain, was reformulated by using the resolvent theory …

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 …

A detailed new upgrade of the FEAST eigensolver targeting non-Hermitian eigenvalue
problems is presented and thoroughly discussed. It aims at broadening the class of …

In this paper, we indicate that the Sakurai-Sugiura method with Rayleigh-Ritz projection
technique, a numerical method for generalized eigenvalue problems, can be extended to …

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 consider an eigensolver for computing eigenvalues in a given domain and the
corresponding eigenvectors of large-scale matrix pencils. The Sakurai-Sugiura (SS) method …

Powerful algorithms have recently been proposed for computing eigenvalues of large
matrices by methods related to contour integrals; best known are the works of Sakurai and …