This paper is about GMRES algorithms for the solution of nonsingular linear systems. We
first consider basic algorithms and study their convergence. We then focus on acceleration …

Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …

Polynomial preconditioning can improve the convergence of the Arnoldi method for
computing eigenvalues. Such preconditioning significantly reduces the cost of …

We develop a reduction multigrid based on approximate ideal restriction (AIR) for use with
asymmetric linear systems. We use fixed-order GMRES polynomials to approximate A ff− 1 …

Low-rank Krylov methods are one of the few options available in the literature to address the
numerical solution of large-scale general linear matrix equations. These routines amount to …

We study first-order methods with preconditioning for solving structured convex optimization
problems. We propose a new family of preconditioners generated by the symmetric …

We present a polynomial preconditioner for solving large systems of linear equations. The
polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is …

Lattice QCD calculations of disconnected quark loop operators are extremely computer time-
consuming to evaluate. To compute these diagrams using lattice techniques, one generally …

In lattice QCD, the calculation of physical quantities from disconnected quark loop
calculations have large variance due to the use of Monte Carlo methods for the estimation of …

Polynomial preconditioners for GMRES and other Krylov solvers are well-known but are
infrequently used in large-scale software libraries or applications. This may be due to …