Numerical Methods in Matrix Computations

verfasst von: Åke Björck

Verlag: Springer International Publishing

Buchreihe : Texts in Applied Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given.

Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Direct Methods for Linear Systems

By a matrix we mean a rectangular array of real or complex numbers ordered in \(m\) rows and \(n\) columns:

Åke Björck

Chapter 2. Linear Least Squares Problems

Abstract

A fundamental task in scientific computing is to estimate parameters in a mathematical model from observations that are subject to errors. A common practice is to reduce the influence of the errors by using more observations than the number of parameters.

Åke Björck

Chapter 3. Matrix Eigenvalue Problems

Abstract

The eigenvalues and eigenvectors of a matrix play an important role in many settings in physics and engineering.

Åke Björck

Chapter 4. Iterative Methods

Abstract

Linear systems \(Ax = b\) of quite large size can be treated using the sparse matrix factorizations described in Sect. 1.7.

Åke Björck

Backmatter

Titel: Numerical Methods in Matrix Computations
verfasst von: Åke Björck
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-05089-8
Print ISBN: 978-3-319-05088-1
DOI: https://doi.org/10.1007/978-3-319-05089-8