A filter diagonalization for generalized eigenvalue problems based on the Sakurai-Sugiura projection method

TL;DR: A parallel eigensolver using contour integration is proposed for generalized eigenvalue problems in molecular simulation, leveraging sparse matrices and numerical integration to compute interior eigenvalues and eigenvectors efficiently in biochemistry applications.

TL;DR: This work develops a new non-Hermitian scheme for the FEAST algorithm, a typical contour-integral based eigensolver for computing the eigenvalues inside a given region in the complex plane.

TL;DR: This paper considers waveguide problems for the Helmholtz equation in two dimensions and standard scattering problems for Maxwell's equations in three dimensions and proposes new BIEs for transmission problems with which one can distinguish true and fictitious eigenvalues easily.

TL;DR: In this paper, the authors presented accurate numerical solutions for nonlinear eigenvalue analysis of three-dimensional acoustic cavities by boundary element method (BEM) and employed a contour integral method, called block Sakurai-Sugiura (SS) method, by which the NEP is converted to a standard linear eigen value problem and the dimension of eigenspace is reduced.

TL;DR: In this paper, an interpretation of Dr. Cornelius Lanczos' iteration method, which he has named ''minimized iterations'' is discussed, expounding the method as applied to the solution of the characteristic matrix equations both in homogeneous and nonhomogeneous form.

TL;DR: This book discusses iterative projection methods for solving Eigenproblems, and some of the techniques used to solve these problems came from the literature on Hermitian Eigenvalue.

TL;DR: A new method for the iterative computation of a few of the extremal eigenvalues of a symmetric matrix and their associated eigenvectors is proposed that has improved convergence properties and that may be used for general matrices.