Numerical solution approach
Abstract:
A.3.1 Ill- conditioned linear systems Probably the best ( or at least the most widely acclaimed) classical method for solving nonsingular linear systems on a computer is Gaussian elimination with pivoting and iterative refinements. This procedure is discussed in great detail in Forsythe and Moler’s book Computer Solution of Linear Algebraic Systems [ 1], and Wilkinson has given extensive treatments of the error analysis of the method in a paper in 1961 [ 2] and in his book Rounding Errors in Algebraic Processes [ 3]. The method is fast, and if the matrix of the system is not too ill-conditioned, it gives correctly rounded approximations to the true solution. By an ill- conditioned system, we mean a system Ax = b ( A.3.1) such that small relative changes in the matrix A or in the right- hand-
