Title :
Determined the Optimum Relaxation Parameter for the 7-point Laplacian
Author_Institution :
Fourth Dept., Southwest China Inst. of Electron. Technol., Chengdu, China
Abstract :
The SOR iteration method for solving linear systems of equations depends upon a relaxation parameter. A well-known theory for determining the relaxation parameter was given by Young for consistently ordered matrices. In this paper, we prove that the matrix of the linear system arisen from the 7-point Laplacian is consistently ordered in both point form and block form. Then by separating variables and solving difference equations, the optimum relaxation parameters of point and block SOR iterations for the system are given for the first time, respectively.
Keywords :
Laplace equations; difference equations; iterative methods; matrix algebra; 7-point Laplacian; SOR iteration method; consistently ordered matrices; difference equations; linear equations systems; linear system matrix; optimum relaxation parameter; Difference equations; Eigenvalues and eigenfunctions; Jacobian matrices; Laplace equations; Linear systems; Mathematical model; 7-point Laplacian; SOR iteration; separate variables; the optimum relaxation parameter;
Conference_Titel :
Computing, Measurement, Control and Sensor Network (CMCSN), 2012 International Conference on
Conference_Location :
Taiyuan
Print_ISBN :
978-1-4673-2033-7
DOI :
10.1109/CMCSN.2012.55
