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

TL;DR: This paper proposes a new extension of the Sakurai-Sugiura projection method (SSPM) for a circumference region on the complex plane, and implements the proposed method in the SLEPc library, and examines its performance on a supercomputer cluster with many-core architecture.

TL;DR: A memory-saving technique for a variant of the Sakurai–Sugiura method that is beneficial in cases where eigenvectors are necessary, because the residual norms of the target eigenpairs can be cheaply computed and monitored during each iteration step of the inner linear solution.

TL;DR: In this article , a block SS-CAA method using a block Arnoldi iteration instead of the subspace iteration was proposed to improve the convergence behavior of the block SS method.

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.