The Error Analysis Of Iterative Algorithms For Large Linear Systems

Suppose Ax = b is a system of linear equations where the matrix A is symmetric positive definite and consistently ordered, which is obtained from a finite difference approximation to an elliptic boundary value problem. This paper derives the bounds for the norm of the errors k= x- xk of the iterative methods in terms of the norms of k = x k - x k~1, k+1= xk+l - x k where x is theexact solution of Ax = b and xk-1, xk, Xk+1 is the iteration vectors, and their inner product.In Chapter 2, we analyze the error bound of the MAOR method, and on the basis we give stopping criteria of the iterative method.In Chapter 3, the error bound of the SAOR method is derived and used as give stopping criteria of the iterative method.In Chapter 4, we get the error bound of the TOR method, and use it as the stopping criteria of the iterative method.