A Weighted GMRES-DR Algorithm for the Linear System of Equations

The GMRES-DR method is an efficient iterative method for the solution of equation sets with large-scale sparse non-symmetric matrix. Based on the analysis of GMRES-DR, in combination with the weighted technology, the velocity of convergence of the GMRES-DR algorithm is accelerated, and it is proven theoretically that the circulatory generations each time of the weighted GMRES-DR algorithm are still Krylov sub-spaces and the numerical experimentation proves the validity of the said algorithm.