<P>THIS BOOK OFFERS AN INTRODUCTION TO THE ALGORITHMIC-NUMERICAL THINKING USING BASIC PROBLEMS OF LINEAR ALGEBRA. BY FOCUSING ON LINEAR ALGEBRA, IT ENSURES A STRONGER THEMATIC COHERENCE THAN IS OTHERWISE FOUND IN INTRODUCTORY LECTURES ON NUMERICS. THE BOOK HIGHLIGHTS THE USEFULNESS OF MATRIX PARTITIONING COMPARED TO A COMPONENT VIEW, LEADING NOT ONLY TO A CLEARER NOTATION AND SHORTER ALGORITHMS, BUT ALSO TO SIGNIFICANT RUNTIME GAINS IN MODERN COMPUTER ARCHITECTURES. THE ALGORITHMS AND ACCOMPANYING NUMERICAL EXAMPLES ARE GIVEN IN THE PROGRAMMING ENVIRONMENT MATLAB, AND ADDITIONALLY – IN AN APPENDIX – IN THE FUTURE-ORIENTED, FREELY ACCESSIBLE PROGRAMMING LANGUAGE JULIA. THIS BOOK IS SUITABLE FOR A TWO-HOUR LECTURE ON NUMERICAL LINEAR ALGEBRA FROM THE SECOND SEMESTER OF A BACHELOR'S DEGREE IN MATHEMATICS.</P>
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This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelor's degree in mathematics.
Folkmar Bornemann is Professor for Numerical Analysis and Scientific Computing at the Technical University of Munich.
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