Exercises in numerical linear algebra and matrix factorizations /

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Bibliographic Details
Author / Creator:	Lyche, Tom, author.
Imprint:	Cham, Switzerland : Springer, [2020]
Description:	1 online resource (xix, 265 pages) : illustrations (some color).
Language:	English
Series:	Texts in computational science and engineering, 1611-0994 ; 23 Texts in computational science and engineering ; 23.
Subject:	Algebras, Linear. Matrices. Computer science -- Mathematics. Numerical analysis. Algebras, Linear. Algorithms. Computer science -- Mathematics. Numerical analysis. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12609364

Hidden Bibliographic Details
Other uniform titles:	Muntingh, Georg, Ryan, Øyvind, Complemented by (work): Lyche, Tom. Numerical linear algebra and matrix factorizations.
ISBN:	303059789X 9783030597894 3030597881 9783030597887
Digital file characteristics:	text file PDF
Notes:	Online resource; title from PDF title page (SpringerLink, viewed January 28, 2021).
Summary:	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.
Other form:	Print version: 9783030597887
Standard no.:	10.1007/978-3-030-59789-4

Table of Contents:

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.

Exercises in numerical linear algebra and matrix factorizations /

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