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...
Improved p-ary codes and sequence families from Galois rings
Ling, San; Özbudak, Ferruh (2005-01-01)
In this paper, a recent bound on some Weil-type exponential sums over Galois rings is used in the construction of codes and sequences. The bound on these type of exponential sums provides a lower bound for the minimum distance of a family of codes over F-p, mostly nonlinear, of length p(m+1) and size p(2) (.) p(m)((D-[D/p2])), where 1 <= D <= p(m/2). Several families of pairwise cyclically distinct p-ary sequences of period p(p(m) - 1) of low correlation are also constructed. They compare favorably with cer...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems
Bozkaya, Canan (2005-03-18)
The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
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...
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: