Open AccessKrylov Methods for Large Sparse Systems: A Comprehensive Overview
Author(s) -
Amanda Zeqiri,
Arben Malko
Publication year - 2021
Publication title -
european scientific journal
Language(s) - English
Resource type - Journals
eISSN - 1857-7881
pISSN - 1857-7431
DOI - 10.19044/esj.2021.v17n17p39
Subject(s) - eigenvalues and eigenvectors , mathematics , convergence (economics) , linear system , computer science , sparse matrix , krylov subspace , mathematical optimization , algorithm , iterative method , computational chemistry , mathematical analysis , physics , quantum mechanics , economics , gaussian , economic growth , chemistry
In this paper are analyzed behavior and properties for different Krylov methods applied in different categories of problems. These categories often include PDEs, econometrics and network models, which are represented by large sparse systems. For our empirical analysis are taken into consideration size, the density of non-zero elements, symmetry/un-symmetry, eigenvalue distribution, also well/ill-conditioned and random systems. Convergence, approximation error and residuals are compared for the full version of methods, some restarted methods and preconditioned methods. Two preconditioners are considered respectively, ILU(0) and IC(0) by using at least five preconditioning techniques. In each case, empirical results show which technique is best to use based on properties of the system and are backed up by general theoretical information already found on Krylov space methods.