Overview
- Many exercises are presented with several solutions (where there may not be a best one)
- Presentation which is tied heavily to that of the textbook “Numerical Linear Algebra and Matrix Factorizations”, published as Vol. 22 of Springer's "Texts in Mathematical Science and Engineering" series
- Contains many examples of implementations in the exercises
Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 23)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
Keywords
About this book
To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students’ learning process.
This book provides precisely this type of supporting material for the textbook “Numerical Linear Algebra and Matrix Factorizations,” published as Vol. 22 of Springer’s Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels.
Reviews
“This is a companion volume to Lyche’s textbook … on numerical linear algebra and matrix factorization. … This combination of this book of exercises and solutions with the original book makes the text more approachable, and the additional teaching present in the solutions is quite valuable. … This book … would also be useful to instructors teaching a linear algebra course at a comparable level. There are a lot of good exercises here that would supplement those in other texts.” (Bill Satzer, MAA Reviews, July 5, 2021)
Authors and Affiliations
About the authors
Tom Lyche is professor emeritus at the University of Oslo. His research interests are in numerical analysis, and splines in approximation theory. He is the author with Jean-Louis Merrien of the book "Exercises in Computational Mathematics with MATLAB" and editor on numerous books on spline methods, computer aided geometric design and approximation theory. He has been a co-organizer of many conferences, in particular the two conference series "Mathematical Methods for Curves and Surfaces" in Norway and "Curves and Surfaces" in France.
Georg Muntingh is a research scientist at the Department of Mathematics and Cybernetics at SINTEF Digital. Jointly with Dr. Tor Dokken, he edited the book “SAGA --- Advances in Shapes, Geometry, and Algebra”, published by Springer in 2014. His research has an interdisciplinary nature and spans a wide range of research fields, with papers published on algebraic geometry, approximation theory, combinatorics, geometric modelling, physics and machine learning.
Øyvind Ryan is associate professor at the Department of Mathematics at the University of Oslo. His main interest lies in book projects on topics building heavily on linear algebra, and he has published the book “Linear Algebra, Signal Processing, and Wavelets – A Unified Approach”, published by Springer in 2019.
Bibliographic Information
Book Title: Exercises in Numerical Linear Algebra and Matrix Factorizations
Authors: Tom Lyche, Georg Muntingh, Øyvind Ryan
Series Title: Texts in Computational Science and Engineering
DOI: https://doi.org/10.1007/978-3-030-59789-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-59788-7Published: 03 November 2020
Softcover ISBN: 978-3-030-59791-7Published: 03 November 2021
eBook ISBN: 978-3-030-59789-4Published: 02 November 2020
Series ISSN: 1611-0994
Series E-ISSN: 2197-179X
Edition Number: 1
Number of Pages: XIX, 265
Number of Illustrations: 2 b/w illustrations, 10 illustrations in colour
Topics: Linear Algebra, Algorithms, Computational Science and Engineering, Numerical Analysis