Improvement of the Preconditioned MRTR Method With Eisenstat's Technique in Real Symmetric Sparse Matrices

The Incomplete Cholesky Conjugate Gradient (ICCG) method is widely used to solve indefinite algebraic equations obtained using an edge-based finite element method. However, when a linear solver based on the minimum residual is used, there is a possibility of reducing the elapsed time for a linear system. This paper shows the performance of the preconditioned minimized residual method based on the three-term recurrence formula of the CG-type (MRTR) method by comparing the MRTR method with the ICCG method for real symmetric sparse matrices. Furthermore, we intend to reduce computational costs by using Eisenstat's technique, and achieve more speed-up by applying a preconditioned residual to the convergence criterion.