A Preconditioned Conjugate Gradient Algorithm for Solving Equation Systems with Non-positive Definite Sparse Matrices

摘要

A new preconditioned conjugate gradient algorithm is presented to solve the system of equations with non-positive definite sparse coefficient matrixes. The algorithm is based on the conjugate gradient method, but employing the incomplete LU factorization approach as the pre-conditioner. By introducing this pre-conditioner the convergence rate of the iterative solution process is increased considerably. The solution results indicate this new preconditioned conjugate gradient algorithm is suitable for solving the equation systems with symmetric non-positive definite sparse matrixes, which appear in the finite element system with anisotropic media.