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2009•Basic Sciences Journal of Textile UniversitiesRequires access

A sufficient and necessary condition of the AOR iterative method for consistently ordered matrices

Da‐Wei Chang

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Abstract

The AOR iterative method for solving linear systems of the form Ax=b is discussed,where A is a large sparse nonsingular matrix.A sufficient and necessary cndition of the AOR iterative method is given in the case that the cofficient matrix A is(1,1) consistently ordered matrix and all square of the eigenvalues of its Jacobi matrix are pure imaginaries or zeroes.In addition,a numerical example is given for illustrating the results.

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The AOR iterative method for solving linear systems of the form Ax=b is discussed,where A is a large sparse nonsingular matrix.A sufficient and necessary cndition of the AOR iterative method is given in the case that the cofficient matrix A is(1,1) consistently ordered matrix and all square of the eigenvalues of its Jacobi matrix are pure imaginaries or zeroes.In addition,a numerical example is given for illustrating the results.

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Available abstract

The AOR iterative method for solving linear systems of the form Ax=b is discussed,where A is a large sparse nonsingular matrix.A sufficient and necessary cndition of the AOR iterative method is given in the case that the cofficient matrix A is(1,1) consistently ordered matrix and all square of the eigenvalues of its Jacobi matrix are pure imaginaries or zeroes.In addition,a numerical example is given for illustrating the results.

Key concepts: Invertible matrix, Iterative method, Mathematics, Eigenvalues and eigenvectors, Matrix (chemical analysis), Applied mathematics, Matrix splitting, Square matrix

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