A CONVERGENCE THEOREM FOR THE JACOBI AND GAUSS-SEIDEL ITERATIONS
Keywords:
Strictly diagonally dominant, Symmetric positive definite, Iterative method, Convergence, Numerical experimentAbstract
This paper treats linear systems whose coefficient matrices are neither strictly diagonally dominant nor symmetric positive definite. By applying a matrix transformation, such a system can be converted into one with a symmetric positive definite coefficient matrix. Sufficient conditions are then established for the convergence of the Jacobi and Gauss–Seidel iterations. Numerical experiments are provided to demonstrate the validity of the theorem.References
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