Optimal linear randomized methods for linear operators in Hilbert spaces
type: Item
instance of: scholarly article
title: Optimal linear randomized methods for linear operators in Hilbert spaces
zbMATH Open document ID: 0754.65049
DOI: 10.1016/0885-064X(92)90032-7
author: Erich Novak
published in: Journal of Complexity
publication date: 1992-09-26T00:00:00Z
review text: Some of the basic questions of information-based complexity are strongly related to \(n\)-width and \(s\)-numbers. These relations were studied in particular by \textit{P. Mathé} [J. Complexity 6, No. 1, 41-66 (1990; Zbl 0723.68047)]. The author studies Monte Carlo methods or randomized methods for linear operators. The main result is the characterization of linear stochastic \(n\)-widths in the case of linear operators in Hilbert spaces.
reviewed by: M. Zuhair Nashed
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 55603
zbMATH Keywords: information-based complexity
zbMATH Keywords: \(s\)-numbers
zbMATH Keywords: Monte Carlo methods
zbMATH Keywords: randomized methods
zbMATH Keywords: linear operators
zbMATH Keywords: linear stochastic \(n\)-widths
zbMATH Keywords: Hilbert spaces
MaRDI profile type: Publication
cites work: DIAMETERS OF SETS IN NORMED LINEAR SPACES AND THE APPROXIMATION OF FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS
cites work: Random approximation of Sobolev embeddings
cites work: s-numbers in information-based complexity
cites work: Deterministic and stochastic error bounds in numerical analysis
cites work: Q3344608
cites work: Q5600030
cites work: Q4275428
cites work: Average case optimality for linear problems
cites work: Q3993279
cites work: Randomization for continuous problems
cites work: Can adaption help on the average?
description: scientific article; zbMATH DE number 55603