Folkmar Bornemann's Books

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.

Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area

Gives concrete examples of how to justify the validity of every single digit of a numerical answer.

This book is about the explicit elimination of fast oscillatory scales in dynamical systems, which is important for efficient computer-simulations and our understanding of model hierarchies. The author presents his new direct method, homogenization in time, based on energy principles and weak convergence techniques. How to use this method is shown in several general cases taken from classical and quantum mechanics. The results are applied to special problems from plasma physics, molecular dynamics and quantum chemistry. Background material from functional analysis is provided and explained to make this book accessible for a general audience of graduate students and researchers.

Gives concrete examples of how to justify the validity of every single digit of a numerical answer.

Book's by Folkmar Bornemann

Numerical Linear Algebra

Numerical Linear Algebra

Scientific Computing with Ordinary Differential Equations

Scientific Computing with Ordinary Differential Equations

The SIAM 100-Digit Challenge

The SIAM 100-Digit Challenge

Numerical Linear Algebra

Numerical Linear Algebra

Homogenization in Time of Singularly Perturbed Mechanical Systems

Homogenization in Time of Singularly Perturbed Mechanical Systems

Scientific Computing with Ordinary Differential Equations

Scientific Computing with Ordinary Differential Equations

The SIAM 100-Digit Challenge

The SIAM 100-Digit Challenge

Homogenization in Time of Singularly Perturbed Mechanical Systems

Homogenization in Time of Singularly Perturbed Mechanical Systems

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