TABLE OF CONTENTS To solve the systems of linear equations using numerical methods, there are two types of methods available. Methods of the first type are called direct methods or elimination methods. This type of method finds the solution in a finite number of steps. These methods are guaranteed to succeed and are recommended for general purposes. Here, we will consider Cramer s rule, the Gaussian elimination method and its variants, the Gauss-Jordan method, and LU decomposition (by Doolittle s, Crout s, and Cholesky methods).
Methods of the second type are called indirect or iterative methods. Iterative methods start with an arbitrary first approximation to the unknown solution x of linear system (3.6) and then improve this estimate in an infinite but convergent sequence of steps. These methods are used for solving large systems of equations. The widely used iterative methods, the Jacobi method , the Gauss-Seidel method , the successive over-relaxation method (SOR), and the conjugate gradient method will be presented in this chapter.
