Tractability of multivariate problems. Volume I: Linear information
type: Item
instance of: scholarly article
title: Tractability of multivariate problems. Volume I: Linear information
zbMATH Open document ID: 1156.65001
DOI: 10.4171/026
author: Erich Novak
author: H. Woźniakowski
published in: EMS Tracts in Mathematics
publication date: 2008-09-03T00:00:00Z
review text: This book is a first of three volumes of the authors devoted to the study of the tractability of multivariate problems. The authors present various existing results obtained by many authors during last years, as well as numerous new results. This volume begins with twelve examples of particular multivariate problems, along with a survey of results in information based complexity that are especially relevant to tractability. This list comprises integration, approximation of \(C^{\infty}\) functions, discrepancy, absolute, relative and normalized errors and Monte Carlo algorithms, among others. The rest of the volume is devoted to the tractability of algorithms using linear information (arbitrary continuous linear functionals). The tractability results are illustrated for many specific multivariate problems, general linear problems including multivariate integration, approximation, as well as a number of specific non-linear problems such as partial differential and integral equations. The book contains a number of open problems that could be of interest to a general audience of mathematicians, and very long list of 296 references.
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 68Q17
Mathematics Subject Classification ID: 68Q25
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 46E22
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 5320563
zbMATH Keywords: curse of dimensionality
zbMATH Keywords: tractability
zbMATH Keywords: high-dimensional numerical problems
zbMATH Keywords: worst case setting
zbMATH Keywords: randomized algorithms
zbMATH Keywords: weighted norms
zbMATH Keywords: product weights
zbMATH Keywords: finite-order weights
zbMATH Keywords: textbook
zbMATH Keywords: information based complexity
zbMATH Keywords: discrepancy
zbMATH Keywords: Monte Carlo algorithms
zbMATH Keywords: linear information
zbMATH Keywords: multivariate integration
reviewed by: Jaromír Antoch
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/026
OpenAlex ID: W1820164671
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description: scientific article; zbMATH DE number 5320563