Numerical Linear Algebra
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Rannacher, Rolf: Numerical Linear Algebra, Heidelberg: Heidelberg University Publishing, 2018.

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ISBN 978-3-946054-99-3 (PDF)
ISBN 978-3-947732-00-5 (Softcover)

Published 04.10.2018.


Rolf Rannacher

Numerical Linear Algebra

Lecture Notes

This introductory text is based on courses within a multi-semester cycle on “Numerical Mathematics” given by the author at the Universities in Saarbrücken and Heidelberg.

In the present part basic concepts of numerical methods are presented for solving linear optimization problems (so-called “Linear Programming”). This includes besides the classical ”Simplex method“ also modern ”Interior-point methods“. As natural extensions methods for convex nonlinear, especially quadratic, optimization problems are discussed.

Theoretical as well as practical aspects are considered. As prerequisite only that prior knowledge is required, which is usually taught in the introductory Analysis, Linear Algebra, and Numerics courses. For facilitating self-learning the book contains theoretical and practical exercises with solutions collected in the appendix.

Rolf Rannacher, retired professor of Numerical Mathematics at Heidelberg University, study of Mathematics at the University of Frankfurt/Main, doctorate 1974, postdoctorate (Habilitation) 1978 at Bonn University – 1979/1980 Vis. Assoc. Professor at the University of Michigan (Ann Arbor, USA), thereafter Professor at Erlangen and Saarbrücken, in Heidelberg since 1988 – field of interest “Numerics of Partial Differential Equations”, especially the “Finite Element Method” and its applications in the Natural Sciences and Engeneering, more than 160 scientific publications.

0 Introduction
1 Linear Algebraic Systems and Eigenvalue Problems
2 Direct Solution Methods
3 Iterative Methods for Linear Algebraic Systems
4 Iterative Methods for Eigenvalue Problems
5 Multigrid Methods
A Solutions of exercises