Gauss type preconditioning techniques for linear systems

Many researchers have considered preconditioners chosen to eliminate the off-diagonal elements of the coefficient matrix of a linear system. In this work, we generalize the left Gauss type preconditioners [Y. Zhang, T.Z. Huang, X.P. Liu, Modified iterative methods for nonnegative matrices and M-matrices linear systems, Comput. Math. Appl. 50 (2005) 1587-1602] which eliminate the strictly lower triangular elements. Right Gauss type preconditioners that eliminate strictly upper triangular elements are proposed in this paper. These Gauss type preconditioners are partly derived from the LU factorization method. Theoretic analysis on spectral radii of the two kinds of Gauss type preconditioners is given. Numerical experiments are used to show the performance of the improved inbuilt left and right Gauss type preconditioning algorithms associated with Jacobi type and Gauss-Seidel type iterative methods.