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

TL;DR: The basic building block library supports an elaborate MPI+X approach that is able to fully exploit hardware heterogeneity while exposing functional parallelism and data parallelism to all other software layers in a flexible way.

TL;DR: This paper proposes block conjugate gradient (CG) type methods for the approximation of CHA1B, in which approximation Xk of linear systems AX=B does not need to be computed explicitly and only the approximation k of k, which is mathematically equivalent to CHXk, will be calculated instead.

TL;DR: In this article, a hybrid Trefftz finite element method (HTFEM) was proposed for analyzing the eigenmodes of optical fibers, and the convergence behavior of the effective indices of optical fiber was examined.

TL;DR: A criterion employing the condition number of eigenvalues as a simple index to distinguish physical solutions from spurious ones in theSSM is presented, and a transcendental equation of a multilayer waveguide obtained by the transfer matrix method is solved by the SSM.

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.