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2010•Basic Sciences Journal of Textile UniversitiesRequires access

The convergence and divergence properties of SOR iterative method for(1,2) consistently ordered matrix

Da‐Wei Chang

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Abstract

Combining the geometry with the algebra,the convergence and divergence properties of SOR iterative methord are discussed for solving the linear system Ax =b with(1,2)consistently ordered matrix,when all the eigenvalues of the B3J are nonpositive and nonnegative respectively.Finally,the analogous results are provided for the case when all the eigenvalues of the B3J are real,then examples are given to illustrate the results,where BJ is the associated Jacobi iterative matrix,A∈Cn×n,x∈Cn,b∈Cn.

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What this paper is about

Combining the geometry with the algebra,the convergence and divergence properties of SOR iterative methord are discussed for solving the linear system Ax =b with(1,2)consistently ordered matrix,when all the eigenvalues of the B3J are nonpositive and nonnegative respectively.Finally,the analogous results are provided for the case when all the eigenvalues of the B3J are real,then examples are given to illustrate the results,where BJ is the associated Jacobi iterative matrix,A∈Cn×n,x∈Cn,b∈Cn.

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Available abstract

Combining the geometry with the algebra,the convergence and divergence properties of SOR iterative methord are discussed for solving the linear system Ax =b with(1,2)consistently ordered matrix,when all the eigenvalues of the B3J are nonpositive and nonnegative respectively.Finally,the analogous results are provided for the case when all the eigenvalues of the B3J are real,then examples are given to illustrate the results,where BJ is the associated Jacobi iterative matrix,A∈Cn×n,x∈Cn,b∈Cn.

Key concepts: Divergence (linguistics), Eigenvalues and eigenvectors, Convergence (economics), Mathematics, Matrix (chemical analysis), Iterative method, Applied mathematics, Pure mathematics

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