Are linear algorithms always good for linear problems?
type: Item
instance of: scholarly article
title: Are linear algorithms always good for linear problems?
zbMATH Open document ID: 0603.65036
DOI: 10.1007/BF02188189
published in: Aequationes Mathematicae
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137159
review text: The question is, if there are linear optimal error algorithms for all linear problems. The answer is no, which is shown in this paper with a general construction, for which every linear algorithm has infinite error, but there is a mildly nonlinear algorithm with finite error, which can be made arbitrarily small if appropriate information is used. As an example the inversion of Laplace transform over a finite interval is considered, a problem arising in remote sensing.
Mathematics Subject Classification ID: 65J05
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 68Q25
zbMATH DE Number: 3974185
zbMATH Keywords: complexity
zbMATH Keywords: information operator
zbMATH Keywords: Laplace transform inversion
zbMATH Keywords: linear optimal error algorithms
zbMATH Keywords: mildly nonlinear algorithm
author: A. G. Werschulz
author: H. Woźniakowski
MaRDI profile type: Publication
cites work: On the optimality of linear methods for operator approximation in convex classes of functions
cites work: Q5531338
cites work: Best approximation of analytic functions from information about their values at a finite number of points
cites work: Linear problems (with extended range) have linear optimal algorithms
cites work: Q3883494
cites work: What is the complexity of ill-posed problems?
cites work: Optimal residual algorithms for linear operator equations
OpenAlex ID: W1980161684
description: scientific article; zbMATH DE number 3974185