New Iterative Method for Positive Real Linear System

A new iterative method is given to the linear system of equations Au=b,where A is large,sparse and nonsymmetric and A~T+A is symmetric and positive definite(SPD) or equivalently A is positive real. The new method is constituted on a basis of mixed splitting of the matrix A,i.e. A=M-S,where M is a symmetric and positive definite matrix and S a skew symmetric matrix. The method needs to choose properly a matrix D which is symmetric and positive definite(SPD) so as to make sure its convergence. Two options of the matrix D are given in form of theorem,based on convergence analysis,with a computation of the method shown through an example. It is proved that the new iterative method is easier to solve the positive real linear system than other methods,e.g. the SOR method.