Lyche / Muntingh / Ryan Exercises in Numerical Linear Algebra and Matrix Factorizations

Erscheinungsjahr 2020
ISBN: 978-3-030-59789-4
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 23, 265 Seiten, eBook

Reihe: Texts in Computational Science and Engineering

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Lyche, Tom

Muntingh, Georg

Ryan, Øyvind

Inhaltsverzeichnis

A Short Review of Linear Algebra.- Diagonally Dominant Tridiagonal Matrices; Three Examples.- Gaussian Eliminationa nd LU Factorizations.- LDL* Factorization and Positive Definite Matrices.- Orthonormal and Unitary Transformations.- Eigenpairs and Similarity Transformations.- The Singular Value Decomposition.- Matrix  Norms and Perturbation Theory for Linear Systems.- Least Squares.- The Kronecker Product .- Fast Direct Solution of a Large Linear System.- The Classical Iterative Methods.- The Conjugate Gradient Method.- Numerical Eigenvalue Problems.- The QR Algorithm.

Über Autor(innen)

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.