Residual Algorithm with Preconditioner for Linear System of Equations

One of the most powerful tools for solving large and sparse systems of linear equation is iterative methods. Their significant advantages like low memory requirements and good approximation properties make them very popular, and they are widely used in applications throughout science and engineering. Residual Algorithm for solving large-scale nonsymmetric linear system of equation which symmetric part is positive (or negative) definite, is evaluated. It uses in a systematic way the residual vector as a search direction, and a spectral steplength. The global convergence is analyzed. A preliminary numerical experimentation is included for showing that the new algorithm is a robust method for solving nonsymmetric linear system and it is competitive with the well-known GMRES and BICGSTAB in number of computed residual and CPU time. The new method for sparse matrix with 12 10 entries has been successfully examined with we use the two preconditioning strategies ILU and SSOR.