A new method for solving line equations with large sparse symmetric and indefinite coefficients matrix

A new preconditioned solution with two controlling parameters for linear equations with large sparse symmetric and indefinite matrix is presented in this paper. Through theoretical analysis, the proper choice of the controlling parameters can make the preconditioned matrix positive definite and close to a unit matrix, and significantly reduce the number of iterations. Numerical examples show that the method can reduce the computation time over 50% more than the conventional incomplete Choleski-conjugate gradient method.