Recent computational developments in Krylov subspace methods for linear systems

V Simoncini, DB Szyld - Numerical Linear Algebra with …, 2007 - Wiley Online Library
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 …

Equation-free multiscale computation: Algorithms and applications

IG Kevrekidis, G Samaey - Annual review of physical chemistry, 2009 - annualreviews.org
In traditional physicochemical modeling, one derives evolution equations at the
(macroscopic, coarse) scale of interest; these are used to perform a variety of tasks …

Numerical solution of saddle point problems

M Benzi, GH Golub, J Liesen - Acta numerica, 2005 - cambridge.org
Large linear systems of saddle point type arise in a wide variety of applications throughout
computational science and engineering. Due to their indefiniteness and often poor spectral …

A survey of numerical linear algebra methods utilizing mixed-precision arithmetic

A Abdelfattah, H Anzt, EG Boman… - … Journal of High …, 2021 - journals.sagepub.com
The efficient utilization of mixed-precision numerical linear algebra algorithms can offer
attractive acceleration to scientific computing applications. Especially with the hardware …

Mixed precision algorithms in numerical linear algebra

NJ Higham, T Mary - Acta Numerica, 2022 - cambridge.org
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 …

[BOOK][B] Handbook of linear algebra

L Hogben - 2006 - books.google.com
The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

[BOOK][B] Lecture notes in computational science and engineering

TJ Barth, M Griebel, DE Keyes, RM Nieminen, D Roose… - 2005 - Springer
The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

Alternating minimal energy methods for linear systems in higher dimensions

SV Dolgov, DV Savostyanov - SIAM Journal on Scientific Computing, 2014 - SIAM
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 …

Excited state properties of point defects in semiconductors and insulators investigated with time-dependent density functional theory

Y **, VW Yu, M Govoni, AC Xu… - Journal of Chemical …, 2023 - ACS Publications
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 …

[BOOK][B] Multilevel block factorization preconditioners: Matrix-based analysis and algorithms for solving finite element equations

PS Vassilevski - 2008 - books.google.com
This monograph is the first to provide a comprehensive, self-contained and rigorous
presentation of some of the most powerful preconditioning methods for solving finite element …