Numerical Linear Algebra and Matrix Factorizations - Tom Lyche

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Auteur(s) : Tom Lyche

Editeur : Springer International Publishing Ag

Langue : Anglais

Parution : 01/03/2021

Format : Moyen, de 350g à 1kg

Nombre de pages : 396

Expédition : 598

Dimensions : 23.5 x 15.5 x 2.2

ISBN : 9783030364700

Résumé :
After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results.Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.

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Biographie:
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. ?yvind 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....

Sommaire:
A Short Review of Linear Algebra.- LU and QR Factorizations.- Eigenpairs and Singular Values.- Matrix Norms and Least Squares.- Kronecker Products and Fourier Transforms.- Iterative Methods for Large Linear Systems.- Eigenvalues and Eigenvectors.- Index.