Optimal P{cyclic Sor
نویسندگان
چکیده
Our purpose in this paper is to extend p{cyclic SOR theory to consistent singular systems and to apply the results to the solution of large scale systems arising, e.g., in queueing network problems in Markov analysis. Markov chains and queueing models lead to structured singular linear systems and are playing an increasing role in the understanding of complex phenomena arising in computer, communication and transportation systems. For certain important classes of singular problems, we develop a convergence theory for p{cyclic SOR, and show how to repartition for optimal convergence. Results by Kontovasilis, Plemmons and Stewart on the concept of convergence of SOR in an extended sense are rigorously analyzed and applied to the solution of periodic Markov chains with period p = 2:
منابع مشابه
Optimal p-Cyclic SOR for Complex Spectra
In this work we consider the Successive Overrelaxation (SOR) method for the solution of a linear system Ax = b, when the matrix A has a block p X P partitioned p-cyclic form and its associated block Jacobi matrix Jp 1s weaJdy cyclic of index p. Following the pioneering work by Young and Varga in the 50s many researchers have considered various cases for the spectrum 0'(Jp ) and have determlned ...
متن کاملA General Theory of Optimal p-Cyclic SOR
The convergence theory of the Successive Overrelaxation (SOR) iterative method for the solution of nonsingular linear systems Ax = b, when the matrix A has a block p X P partitioned p-cyclic form, is well documented. However, when A is singular the corresponding theory is far behind that for the nonsingular case. Our purpose in this paper is to extend the p-cyclic SOR theory to consistent singu...
متن کاملOptimal Semi-Iterative Methods for Complex SOR with Results from Potential Theory
We consider the application of semi-iterative methods (SIM) to the standard (SOR) method with complex relaxation parameter ω, under the following two assumptions: (1) the associated Jacobi matrix J is consistently ordered and weakly cyclic of index 2, and (2) the spectrum σ(J ) of J belongs to a compact subset of the complex plane C, which is symmetric with respect to the origin. By using resul...
متن کاملExact SOR Convergence Regions for a General Class of p-Cyclic Matrices
Linear systems whose associated block Jacobi iteration matrix B is weakly cyclic generated by the cyclic permutation u = (ul , 02,. . . , up) in the spirit of Li and Varga are considered. Regions of convergence for the corresponding block pcyclic SOR method are derived and the exact convergence domains for real spectra, u(BP), of the same sign are obtained. Moreover, analytical expressions for ...
متن کامل