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Selected Topics in Approximation and Computation$
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Marek A. Kowalski, Krzystof A. Sikorski, and Frank Stenger

Print publication date: 1995

Print ISBN-13: 9780195080599

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195080599.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 21 September 2021

Optimal Approximation Methods

Optimal Approximation Methods

Chapter:
(p.259) Chapter 7 Optimal Approximation Methods
Source:
Selected Topics in Approximation and Computation
Author(s):

Marek A. Kowalski

Krzysztof A. Sikorski

Frank Stenger

Publisher:
Oxford University Press
DOI:10.1093/9780195080599.003.00010

In this chapter we outline a theory of optimal computational methods for general, nonlinear approximation problems. We define the notions of optimal algorithms and information, and we analyze the classes of parallel and sequential methods. We put special emphasis on linear problems as well as linear and spline algorithms. Several relationships between optimal methods and n-widths and s-numbers are also exhibited.

Keywords:   absolute error criterion, cardinality, global diameter, information, linear algorithm, nonadaptive information, optimal information, parallel information, restriction operator, sequential information

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