A Class of Direct and Effective Methods for Solving Linear Systems

Based On Huang Method, a class of improved methods is given for solving ill-conditioned linear systems directly and effectively. An Onsingular upper triaugular matrix R, formed and revised step by step in the process of iteration, is introduced. The linear independence of matrix AR's column vectors is much stronger than that of the original coefficient matrix A. The solution space of the systems is not changed, therefore the column vectors of matrix AR Can be used to obtain a good orthogonal basis of the systems with ordinary orthogonal method and finally the solution of the systems. Numerical examples show that these methods are more efficient than ordinary orthogonal methods.