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Numerical linear algebra and matrix ...

Lyche, Tom.

Numerical linear algebra and matrix factorizations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical linear algebra and matrix factorizationsby Tom Lyche.
Author:	Lyche, Tom.
Published:	Cham :Springer International Publishing :2020.
Description:	xxiii, 371 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Algebras, Linear.
Online resource:	https://doi.org/10.1007/978-3-030-36468-7
ISBN:	9783030364687$q(electronic bk.)

Numerical linear algebra and matrix factorizations
Lyche, Tom.

Numerical linear algebra and matrix factorizations[electronic resource] /by Tom Lyche. - Cham :Springer International Publishing :2020. - xxiii, 371 p. :ill., digital ;24 cm. - Texts in computational science and engineering,221611-0994 ;. - Texts in computational science and engineering ;6..

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.

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.

ISBN: 9783030364687$q(electronic bk.)

Standard No.: 10.1007/978-3-030-36468-7doiSubjects--Topical Terms:

183087
Algebras, Linear.

LC Class. No.: QA184 / .L934 2020

Dewey Class. No.: 512.5

Numerical linear algebra and matrix factorizations
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245 1 0 $a Numerical linear algebra and matrix factorizations $h [electronic resource] / $c by Tom Lyche.
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505 0 $a 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.
520 $a 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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