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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.
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