ABSTRACT

We have encountered Gauss elimination methods for solving linear systems. These work well for moderately sized systems, up to a few thousand equations; in particular if they do not pose numerical problems. Ill-conditioned problems are more efficiently attacked using the Householder method. Huge linear systems up to a million equations are more successfully solved with iterative methods. We introduce Gauss-Jacobi and Gauss-Seidel methods. Often, these linear systems are defined by a sparse matrix, one that has many zero entries. All these alternative methods are the topics of this chapter. Furthermore, we introduce matrix norms and the condition number. Sketches and figures illustrate the concepts.