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

TL;DR: In this article, the authors present a detailed numerical analysis of the FEAST algorithm and show that it can be interpreted as an accelerated subspace iteration algorithm in conjunction with the Rayleigh-Ritz procedure.

TL;DR: This work proposes improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximation based on the work of Zolotarev, and improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel.

TL;DR: In this paper, the Rayleigh-Ritz-type approach of the contour integral eigensolver is extended to general applicability to non-Hermitian systems, which can extract only the eigenvalues in a given domain.

TL;DR: A detailed new upgrade of the FEAST eigensolver targeting non-Hermitian eigenvalue problems is presented and thoroughly discussed, aiming at broadening the class of eigenproblems that can be addressed within the framework of theFEAST algorithm.

TL;DR: Turnbull and Aitken as mentioned in this paper introduced the theory of Canonical Matrices, a new type of algebra reminiscent of such authors as Salmon and Weber, in which the fundamental laws of ordinary algebra are not necessarily valid.

TL;DR: In this paper, a new version of the filter diagonalization method of diagonalizing large real symmetric Hamiltonian matrices is presented, which produces a small set of adapted basis functions by applying the Chebyshev polynomial expansion of the Green's function on a generic initial vector χ. The small Hamiltonian, H and overlap, S, matrices would then be evaluated in this adapted basis and the corresponding generalized eigenvalue problem would be solved yielding the desired spectral information.

TL;DR: In this article, the residual vectors can be made mutually orthogonal by means of a two-term recursion relation which leads to the well-known conjugate gradient (CG) method.

TL;DR: In this paper, a Rayleigh-Ritz type eigensolver for finding a limited set of eigenvalues and their corresponding eigenvectors in a certain region of generalized eigen-value problems is considered.