Many advances in the development of Krylov subspace methods for the iterative solution of
linear systems during the last decade and a half are reviewed. These new developments …

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer
attractive acceleration to scientific computing applications. Especially with the hardware …

Today's floating-point arithmetic landscape is broader than ever. While scientific computing
has traditionally used single precision and double precision floating-point arithmetics, half …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

We propose algorithms for the solution of high-dimensional symmetrical positive definite
(SPD) linear systems with the matrix and the right-hand side given and the solution sought in …

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 …

We present a formulation of spin-conserving and spin-flip hybrid time-dependent density
functional theory (TDDFT), including the calculation of analytical forces, which allows for …

We provide a general framework for the understanding of inexact Krylov subspace methods
for the solution of symmetric and nonsymmetric linear systems of equations, as well as for …

In lattice quantum chromodynamics (QCD) computations a substantial amount of work is
spent in solving discretized versions of the Dirac equation. Conventional Krylov solvers …

The Lanczos method is an iterative procedure to compute an orthogonal basis for the Krylov
subspace generated by a symmetric matrix A and a starting vector v. An interesting …