Practical Linear Algebra, 3rd Edition

Chapter 13

Alternative System Solvers

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 below. Huge linear systems (up to a million equations) are more successfully solved with iterative methods. Often times, these linear systems are defined by a sparse matrix, one that has many zero entries, as is illustrated in Figure 13.1. All these alternative methods are the topics of this chapter.

Figure 13.1

A sparse ...