54 citations · 91 across the 9 of their papers we have counts for
15 papers
Preconditioned steepest descent-like methods for symmetric indefinite systems
Eugene Vecharynski, Andrew Knyazev
This paper addresses the question of what exactly is an analogue of the preconditioned steepest descent (PSD) algorithm in the case of a symmetric indefinite system with an SPD pre…
Preconditioned iterative methods for eigenvalue counts
Eugene Vecharynski, Chao Yang
We describe preconditioned iterative methods for estimating the number of eigenvalues of a Hermitian matrix within a given interval. Such estimation is useful in a number of applic…
A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems
Ruipeng Li, Yuanzhe Xi, Eugene Vecharynski +2
Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywh…
A generalization of Saad's bound on harmonic Ritz vectors of Hermitian matrices
Eugene Vecharynski
We prove a Saad's type bound for harmonic Ritz vectors of a Hermitian matrix. The new bound reveals a dependence of the harmonic Rayleigh--Ritz procedure on the condition number of…
An efficient basis set representation for calculating electrons in molecules
Jeremiah R. Jones, Francois-Henry Rouet, Keith V. Lawler +9
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation…
Generalized preconditioned locally harmonic residual method for non-Hermitian eigenproblems
Eugene Vecharynski, Chao Yang, Fei Xue
We introduce the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly us…