Numerical Linear Algebra

This introductory text is based on lectures from a multi-semester course on 'Numerical Mathematics' that the author has given at the universities of Saarbrücken and Heidelberg. The present volume develops the concepts of numerical methods for solving linear optimization problems (so-called 'linear programs'). This includes not only the classical 'Simplex method' but also more modern 'Interior Point methods'. As natural extensions, methods for convex nonlinear, specifically quadratic optimization problems are also discussed. Both theoretical-mathematical and practical aspects are taken into account. Understanding the content requires only the background knowledge typically provided in introductory courses on analysis, linear algebra, and numerical methods. To facilitate self-study, theoretical and practical exercises with solutions are included in the appendix.