Modified iterative methods for linear systems of equations

An extension of the modified Jacobi and Gauss-Seidel methods for systems of linear equations has been introduced. The convergence properties of the proposed methods have been analyzed and compared with the classical and modified methods. The numerical results obtained for some linear systems show that the extended modified methods are superior to other modified iterative methods.


Improved parallel preconditioners for multidisciplinary topology optimisations
AKAY, HASAN UMUR; Oktay, E.; Manguoğlu, Murat; Sivas, A. A. (2016-01-01)
Two commonly used preconditioners were evaluated for parallel solution of linear systems of equations with high condition numbers. The test cases were derived from topology optimisation applications in multiple disciplines, where the material distribution finite element methods were used. Because in this optimisation method, the equations rapidly become ill-conditioned due to disappearance of large number of elements from the design space as the optimisations progresses, it is shown that the choice for a su...
Multi-symplectic integration of coupled non-linear Schrodinger system with soliton solutions
AYDIN, AYHAN; Karasözen, Bülent (2009-01-01)
Systems of coupled non-linear Schrodinger equations with soliton solutions are integrated using the six-point scheme which is equivalent to the multi-symplectic Preissman scheme. The numerical dispersion relations are studied for the linearized equation. Numerical results for elastic and inelastic soliton collisions are presented. Numerical experiments confirm the excellent conservation of energy, momentum and norm in long-term computations and their relations to the qualitative behaviour of the soliton sol...
Parallel preconditioners for solutions of dense linear systems with tens of millions of unknowns
Malas, Tahir; Ergül, Özgür Salih; Gurel, Levent (2007-11-09)
We propose novel parallel preconditioning schemes for the iterative solution of integral equation methods. In particular, we try to improve convergence rate of the ill-conditioned linear systems formulated by the electric-field integral equation, which is the only integral-equation formulation for targets having open surfaces. For moderate-size problems, iterative solution of the neat-field system enables much faster convergence compared to the widely used sparse approximate inverse preconditioner. For larg...
Backward stochastic differential equations and Feynman-Kac formula in the presence of jump processes
İncegül Yücetürk, Cansu; Yolcu Okur, Yeliz; Hayfavi, Azize; Department of Financial Mathematics (2013)
Backward Stochastic Differential Equations (BSDEs) appear as a new class of stochastic differential equations, with a given value at the terminal time T. The application area of the BSDEs is conceptually wide which is known only for forty years. In financial mathematics, El Karoui, Peng and Quenez have a fundamental and significant article called “Backward Stochastic Differential Equations in Finance” (1997) which is taken as a groundwork for this thesis. In this thesis we follow the following steps: Firstl...
New bent functions from permutations and linear translators
MESNAGER, sihem; ONGAN, pınar; Özbudak, Ferruh (2017-04-12)
Starting from the secondary construction originally introduced by Carlet ["On Bent and Highly Nonlinear Balanced/Resilient Functions and Their Algebraic Immunities", Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 2006], that we shall call "Carlet` ssecondary construction", Mesnager has showed how one can construct several new primary constructions of bent functions. In particular, she has showed that three tuples of permutations over the finite field F2m such that the inverse of their sum...
Citation Formats
B. Karasözen, “Modified iterative methods for linear systems of equations,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, pp. 179–196, 1998, Accessed: 00, 2020. [Online]. Available: