Computational error and complexity in science and engineering
type: Item
instance of: scholarly article
title: Computational error and complexity in science and engineering
zbMATH Open document ID: 1076.65045
author: V. Lakshmikantham
author: Syamal K. Sen
published in: Mathematics in Science and Engineering
publication date: 2005-05-11T00:00:00Z
full work available at URL: http://www.sciencedirect.com/science/book/9780444518606
review text: This monograph for graduates in engineering, computer science and mathematics focuses on error and complexity. Both topics allow to estimate the quality and the cost of the results produced by an algorithm. The nearly 250 pages consist of six chapters with further subdivisions. Chapter 1 introduces into the subject, discusses the distinction between science and engineering and considers capability, limitation, tools, types and models of computation. Moreover, it gives a first impression of computer representable numbers and highlights problem solving. The next two chapters are devoted to the two main topics of the book: Chapter 2 is an exposition of all that is connected with error. Among others it introduces errors, discusses the importance of relative errors, defines computable errors and shows how to compute and to estimate them. Complexity is the core of Chapter 3. Turing machines, Gödel's incompleteness theorem, P- and NP-problems, NP-completeness and probabilistic complexity are some of the keywords appearing here. Chapter 4 deals with errors and approximations in digital computers. Number representation is widely discussed including the importance of the base 2 system, floating point numbers and details of the IEEE 754 standard. Chapter 5 presents several numerical algorithms together with their error and complexity. Topics are interpolation, direct and iterative linear system solvers including singular systems, eigenproblems, linear programming with Karmarkar's algorithm, numerical differentiation and integration. Error and complexity in error-free computation as well as that in parallel and probabilistic computations are described in Chapter 6. Examples are included throughout the text to illustrate the underlying ideas. Sometimes program segments in Matlab are added. References are listed at the end of each chapter.
reviewed by: Günter Mayer
Mathematics Subject Classification ID: 65Gxx
Mathematics Subject Classification ID: 68Qxx
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 68-02
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 00A06
Mathematics Subject Classification ID: 65Fxx
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 2167058
zbMATH Keywords: computational error
zbMATH Keywords: complexity
zbMATH Keywords: IEEE 754
zbMATH Keywords: textbook
zbMATH Keywords: NP-problem
zbMATH Keywords: P-problem
zbMATH Keywords: probabilistic computation
zbMATH Keywords: parallel computation
zbMATH Keywords: floating point numbers
zbMATH Keywords: Turing machines
zbMATH Keywords: singular systems
zbMATH Keywords: eigenproblems
zbMATH Keywords: linear programming
zbMATH Keywords: Karmarkar's algorithm
zbMATH Keywords: numerical differentiation
describes a project that uses: Matlab
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2167058