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Small errors imply large evaluation instabilities

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Bibliographic Details
Main Author: Robert, Schaback
Format: Book
Language:English
Published: Springer 2023
Subjects:
Numerical analysts
Trade-off Principle
Online Access:https://link.springer.com/article/10.1007/s10444-023-10026-2
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7491
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spelling oai:localhost:PNK-74912023-04-04T07:11:03Z Small errors imply large evaluation instabilities Robert, Schaback Numerical analysts Trade-off Principle CC BY Numerical analysts and scientists working in applications often observe that once they improve their techniques to get a better accuracy, some instability of the evaluation creeps in through the back door. This paper shows for a large class of numerical methods that such a Trade-off Principle between error and evaluation stability is unavoidable. It is an instance of a no free lunch theorem. Here, evaluation is the mathematical map that takes input data to output data. This is independent from the numerical routine that calculates the output. Therefore, evaluation stability is different from computational stability. The setting is confined to recovery of functions from data, but it includes solving differential equations by writing such methods as a recovery of functions under constraints imposed by differential operators and boundary values. 2023-04-04T07:11:03Z 2023-04-04T07:11:03Z 2023 Book https://link.springer.com/article/10.1007/s10444-023-10026-2 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7491 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic Numerical analysts
Trade-off Principle
spellingShingle Numerical analysts
Trade-off Principle
Robert, Schaback
Small errors imply large evaluation instabilities
description CC BY
format Book
author Robert, Schaback
author_facet Robert, Schaback
author_sort Robert, Schaback
title Small errors imply large evaluation instabilities
title_short Small errors imply large evaluation instabilities
title_full Small errors imply large evaluation instabilities
title_fullStr Small errors imply large evaluation instabilities
title_full_unstemmed Small errors imply large evaluation instabilities
title_sort small errors imply large evaluation instabilities
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s10444-023-10026-2
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7491
_version_ 1762274899498369024
score 8.891145

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