A New Method for Solving Linear Equations with Large Sparse Symmetric and Non-positively Definite Coefficient Matrix

摘要

A new preconditioned solution with two controlling parameters for linear equations with large sparse symmetric and non-positively definite matrix is presented in this paper. Through theoretical analysis, toe proper choice of the controlling parameter can make the preconditioned matrix positively definite and approach the unit matrix, and reduce the number of iteration obviously. Numerical examples show that the method can reduce the computation time over 59% than the conventional ICCG method.