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

TL;DR: In this paper, a numerical algorithm to calculate exact finite-temperature spectra of many-body lattice Hamiltonians is formulated by combining the typicality approach and the shifted Krylov subspace method.

TL;DR: This work proposes a novel complex moment-based supervised eigenmap including multiple eigenvectors for dimensionality reduction and provides a general formulation for matrix trace optimization methods to incorporate with ridge regression, which models the linear dependency between covariate variables and univariate labels.

TL;DR: Numerical experiments indicate that the proposed block SS-CAA method has higher performance compared with traditional complex moment-based nonlinear eigensolvers, i.e., the block SS–Hankel and Beyn methods.

TL;DR: An efficient way to calculate the electronic structure of large systems is proposed by combining a large-scale first-principles density functional theory code, Conquest, and an efficient interior eigenproblem solver, the Sakurai-Sugiura 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.