Iterative refinement of the Gauss-Jordan method, in ill conditioned systems.
Abstract
In this paper, an iterative algorithm is constructed to improve the solution of a system of linear equations, of the form Ax = b, when it is solved using the Gauss-Jordan Method and by using finite arithmetic. Understanding the functioning of the algorithm, showing its scope and analyzing how it is deduced, is achieved through the concept of matrix norm, together with some of its properties. The concept of the condition number of a matrix is introduced, and are found bounds for it by using the matrix norms. Finally, it is explained the iterative algorithm of the Refinement, showing the power of this one, when it is solved a system of linear equations ill conditioned.
Keywords
Matrix norm, condition numbers, Refinement Method.
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