{"content":[{"text":"ESJ Natural/Life/Medical Sciences","bbox":{"left":0.139581,"top":0.104722,"width":0.344675,"height":0.022813000000000014}},{"text":"Krylov Methods for Large Sparse Systems: \n A Comprehensive Overview","bbox":{"left":0.249341,"top":0.145284,"width":0.500896,"height":0.048764}},{"text":"Amanda Zeqiri \n Arben Malko \n University of Tirana, Faculty of Natural Sciences, \n Department of Applied Mathematics, Albania","bbox":{"left":0.267481,"top":0.210009,"width":0.464651,"height":0.07717800000000002}},{"text":"Doi:10.19044/esj.2021.v17n17p39","bbox":{"left":0.139581,"top":0.303577,"width":0.269499,"height":0.018237999999999976}},{"text":"Submitted: 12 April 2021 \n Accepted: 11 May 2021 \n Published: 31 May 2021","bbox":{"left":0.139581,"top":0.338333,"width":0.19860700000000003,"height":0.04969899999999999}},{"text":"Copyright 2021 Author(s) \n Under Creative Commons BY-NC-ND \n 4.0 OPEN ACCESS","bbox":{"left":0.534322,"top":0.338333,"width":0.30304600000000004,"height":0.04969899999999999}},{"text":"Cite As: \n Zeqiri A. & Malko A. (2021). Krylov Methods for Large Sparse Systems: A Comprehensive \n Overview. European Scientific Journal, ESJ, 17(17), 39. \n https://doi.org/10.19044/esj.2021.v17n17p39","bbox":{"left":0.139581,"top":0.405944,"width":0.7209429999999999,"height":0.06428199999999995}},{"text":"Abstract \n In this paper are analyzed behavior and properties for different Krylov \n methods applied in different categories of problems. These categories often \n include PDEs, econometrics and network models, which are represented by \n large sparse systems. For our empirical analysis are taken into consideration \n size, the density of non-zero elements, symmetry/un-symmetry, eigenvalue \n distribution, also well/ill-conditioned and random systems. Convergence, \n approximation error and residuals are compared for the full version of \n methods, some restarted methods and preconditioned methods. Two \n preconditioners are considered respectively, ILU(0) and IC(0) by using at least \n five preconditioning techniques. In each case, empirical results show which \n technique is best to use based on properties of the system and are backed up \n by general theoretical information already found on Krylov space methods.","bbox":{"left":0.139581,"top":0.48677,"width":0.7211480000000001,"height":0.24884699999999998}},{"text":"Keywords: Krylov methods, numerical experiments, sparse linear systems, \n preconditioning","bbox":{"left":0.139581,"top":0.751364,"width":0.720574,"height":0.04091599999999995}},{"text":"Introduction \n Krylov methods are a large class of iterative algorithms that work with \n finite matrices and vectors in real and complex arithmetic. Many applications, \n which include solving linear systems, eigenvalue problems, and singular value","bbox":{"left":0.139581,"top":0.80867,"width":0.720923,"height":0.07835000000000003}},{"text":"www.eujournal.org","bbox":{"left":0.141209,"top":0.935437,"width":0.149033,"height":0.015140000000000042}},{"text":"39","bbox":{"left":0.837636,"top":0.932942,"width":0.023023000000000016,"height":0.01824099999999995}}],"images_bbox":[],"images_bbox_not_text_overlap":[]}