2003, Vol 4, No 2
http://hdl.handle.net/123456789/3491
Fri, 19 Apr 2019 15:07:06 GMT2019-04-19T15:07:06ZUsing ω-circulant matrices for the preconditioning of Toeplitz Systems
http://hdl.handle.net/123456789/3613
Using ω-circulant matrices for the preconditioning of Toeplitz Systems
Fischer, Rainer; Huckle, Thomas
Toeplitz systems can be solved efficiently by using iterative methods such as the conjugate gradient algorithm. If a suitable preconditioner is used, the overall cost of the method is O(n log(n)) arithmetic operations. Circulant matrices are frequently employed for the preconditioning of Toeplitz systems.They can be chosen as preconditioners themselves, or they can be used for the computation of approximate inverses. In this article, we take the larger class of ω-circulant matrices instead of the well-known circulants to extend preconditioners of both types.This extension yields an additional free parameter ω which can be chosen in a way that speeds up convergence of the conjugate gradient method. The additional computational effort arising from the use of ω-circulant instead of circulant matrices is low.
url: http://sjam.selcuk.edu.tr/sjam/article/view/128
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/123456789/36132003-01-01T00:00:00ZOptimum spectral parameter and convergency for stationary iterative methods in the case of three-diagonal SLAE
http://hdl.handle.net/123456789/3612
Optimum spectral parameter and convergency for stationary iterative methods in the case of three-diagonal SLAE
Kulikov, Sergey
The modified stationary iterative methods of the solution of system of the linear algebraic equations (SLAE) are considered.For SLAE with a three-diagonal matrix with constant factors it is shown, that eigenvalues of modified matrices or the operator, participating in series of simple iteration, are expressed through roots of Chebyshev polynomials of the second kind. On this basis strict expressions through factors of an initial matrix for optimum parameter of convergence and spectral radius are found. So for Successive Overrelaxation method strict expression for the optimum parameter of convergence w0 laying on an interval (0,2) is found. It is shown, that convergence of the optimum modified series essentially improves.
url: http://sjam.selcuk.edu.tr/sjam/article/view/129
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/123456789/36122003-01-01T00:00:00ZVolterra integral equation method for solving some hyperbolic equation problems
http://hdl.handle.net/123456789/3611
Volterra integral equation method for solving some hyperbolic equation problems
Yakhno, Valery G.; Işık, Ali
The Cauchy problem for a hyperbolic equation with function coefficients of the first partial derivatives with respect to time and space variables is considered. It is proved by Sobolev's method that solution of this problem satisfies a 3-D Volterra integral equation. Using this fact the uniqueness theorem for an inverse problem is proved.
url: http://sjam.selcuk.edu.tr/sjam/article/view/130
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/123456789/36112003-01-01T00:00:00ZSimulation of electromagnetic wave propagation in anisotropic media
http://hdl.handle.net/123456789/3610
Simulation of electromagnetic wave propagation in anisotropic media
Yakhno, Valery G.; Yakhno, Tatyana; Kasap, Mustafa
Explicit formulas for fundamental and generalized solutions of the Cauchy problem for Maxwell's system are obtained for the case when the dielectric permeability is a symmetric positive definite matrix, the magnetic permeability is a positive constant, the conductivity vanished. The visualization of electromagnetic wave propagation made using these formulas by MatLAB, C++.
url: http://sjam.selcuk.edu.tr/sjam/article/view/131
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/123456789/36102003-01-01T00:00:00Z