Numerical Linear Algebra and Matrix Factorizations

1. Auflage 2020
ISBN: 978-3-030-36467-0
Verlag: Springer International Publishing

Buch, Englisch, Band 22, 371 Seiten, Book w. online files / update, Format (B × H): 160 mm x 241 mm, Gewicht: 758 g

Reihe: Texts in Computational Science and Engineering

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. 

Zielgruppe

Graduate

Autoren/Hrsg.

Lyche, Tom

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

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.

Über Autor(innen)

The author has a long experience at the university level, teaching numerical analysis, numerical linear algebra and matrix theory, mathematical optimization, approximation theory, and computer aided geometric design. 
He has received the Dagstuhl foundation’s John Gregory Memorial Award for "Outstanding contributions to geometric modeling" and is a member of Norwegian Academy of Science and Letters. 
He has published more than 90 papers in leading international journals and refereed proceedings, edited 17 books and is on the editorial board of 4 international journals. Jointly with Prof. Jean-Louis Merrien,  he has published the book “Exercises in Computational Mathematics with MATLAB “ published by Springer in 2014.