ABSTRACT
In the first 3 chapters the concepts and the ideas involved in linear algebra have been given. The utility and the beauty of linear algebra lies in the fact that it can handle linear equations having thousands of variables. Since the solving of systems is not manually possible, the support of computational techniques involving algorithms that can be evaluated by machines is essential. In this context this chapter plays an important role by introducing methods that simplify the linear system either to a triangular form or diagonal form thus making the approach for finding the solution comparatively easy.
In Section 4.2 the problems and the limitations of computation that depend on the computer are briefly touched upon. Section 4.3 deals with direct methods for solving a system of linear equations and Section 4.4 concentrates on iterative methods to achieve these. As orthogonal transformation preserves norms, new errors do not creep in when they are utilized, hence the Householder transformation and plane rotation transformation are described in Section 4.5 and Section 4.6 respectively. Section 4.7 deals with QR decomposition using Householder transformation. Finding the bounds for the eigen values and the power method for finding the largest eigen value form the content of Section 4.8. A brief description of Krylov subspace methods is given in Section 4.9.
