Numerical Linear Algebra: A Concise Introduction with MATLAB and Julia

✍ Scribed by Folkmar Bornemann (auth.)

• Publisher: Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 157
• Series: Springer Undergraduate Mathematics Series
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-x
Computing with Matrices (Folkmar Bornemann)....Pages 1-19
Matrix Factorization (Folkmar Bornemann)....Pages 21-37
Error Analysis (Folkmar Bornemann)....Pages 39-67
Least Squares (Folkmar Bornemann)....Pages 69-74
Eigenvalue Problems (Folkmar Bornemann)....Pages 75-97
Back Matter ....Pages 99-153

✦ Subjects

Linear and Multilinear Algebras, Matrix Theory