Abstract:
The Preconditioned Conjugate Gradient (PCG) method is implemented to solve the system with 9 diagonal entries generated from a 9-point finite difference approximation of the self-adjoint elliptic partial differential equation using an incomplete matrix decomposition. A simpler matrix decomposition for such a linear system is also proposed with a main advantage that it preserves the symmetry of the original matrix, and is easy to implement. Results of the numerical experiments and comparison with other iterative methods are presented.
Description:
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