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2020•FUDMA Journal of SciencesOpen access

IMPROVING PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR L-MATRICES

Abdulrahman Ndanusa, Bryn David, B. B. Ayantola, A. W. Abubakar

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Abstract

The Gauss-Seidel is a well-known iterative method for solving the linear system Ax = b.  Convergence of this method is guaranteed for linear systems whose coefficient matrix  is strictly or irreducibly diagonally dominant, Hermitian positive definite and invertible H -matrix. In this current work, a preconditioned version of the Gauss-Seidel method is used to accelerate the convergence of this iterative method towards the solution of linear system  under mild conditions imposed on A . Convergence theorems on preconditioned Gauss-Seidel iterative method are advanced and proved. The superiority of Preconditioned Gauss-Seidel method is demonstrated by solving some numerical examples.

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What this paper is about

The Gauss-Seidel is a well-known iterative method for solving the linear system Ax = b.  Convergence of this method is guaranteed for linear systems whose coefficient matrix  is strictly or irreducibly diagonally dominant, Hermitian positive definite and invertible H -matrix. In this current work, a preconditioned version of the Gauss-Seidel method is used to accelerate the convergence of this iterative method towards the solution of linear system  under mild conditions imposed on A . Convergence theorems on preconditioned Gauss-Seidel iterative method are advanced and proved. The superiority of Preconditioned Gauss-Seidel method is demonstrated by solving some numerical examples.

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Available abstract

The Gauss-Seidel is a well-known iterative method for solving the linear system Ax = b.  Convergence of this method is guaranteed for linear systems whose coefficient matrix  is strictly or irreducibly diagonally dominant, Hermitian positive definite and invertible H -matrix. In this current work, a preconditioned version of the Gauss-Seidel method is used to accelerate the convergence of this iterative method towards the solution of linear system  under mild conditions imposed on A . Convergence theorems on preconditioned Gauss-Seidel iterative method are advanced and proved. The superiority of Preconditioned Gauss-Seidel method is demonstrated by solving some numerical examples.

Key concepts: Gauss–Seidel method, Mathematics, Iterative method, Diagonally dominant matrix, Coefficient matrix, Convergence (economics), Invertible matrix, Applied mathematics

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