Algorithms for the solution of linear systems of algebraic equations arise in one way or another in almost every scientific problem. This happens because such systems are of such a fundamental nature. For example, nonlinear problems are typically reduced to a sequence of linear problems, and differential equations are discretized to a finite dimensional system of equations.

The present book deals primarily with the numerical solution of linear systems. The solution algorithms considered are mainly iterative methods. Some results related to the estimate of eigenvalues (of importance for estimating the rate of convergence of iterative solution methods, for instance), are also presented. Both the algorithms and their theory are discussed. Many phenomena that can occur in the numerical solution of the above problems require a good understanding of the theoretical background of the methods. This background is also necessary for the further development of algorithms. It is assumed that the reader has a basic knowledge of linear algebra such as properties of sets of linearly independent vectors, elementary matrix algebra, and basic properties of determinants.

The first six or seven chapters and Appendix A can be (and have been) used as a textbook for an introductory course in numerical linear algebra, but this material demands students who are not afraid of theory. The theory is presented so that it can be followed even in selfstudy.