The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F09%3A00206582" target="_blank" >RIV/00216208:11320/09:00206582 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/09:00329240 RIV/46747885:24220/09:#0001327

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data

Popis výsledku v původním jazyce

Regularization techniques based on the Golub-Kahan iterative bidiagonalization belong among popular approaches for solving large ill-posed problems. First, the original problem is projected onto a lower dimensional subspace using the bidiagonalization algorithm, which by itself represents a form of regularization by projection. The projected problem, however, inherits a part of the ill-posedness of the original problem, and therefore some form of inner regularization must be applied. Stopping criteria for the whole process are then based on the regularization of the projected (small) problem. In this paper we consider an ill-posed problem with a noisy right-hand side (observation vector), where the noise level is unknown. We show how the information from the Golub-Kahan iterative bidiagonalization can be used for estimating the noise level. Such information can be useful for constructing efficient stopping criteria in solving ill-posed problems.

Název v anglickém jazyce

The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data

Popis výsledku anglicky

Regularization techniques based on the Golub-Kahan iterative bidiagonalization belong among popular approaches for solving large ill-posed problems. First, the original problem is projected onto a lower dimensional subspace using the bidiagonalization algorithm, which by itself represents a form of regularization by projection. The projected problem, however, inherits a part of the ill-posedness of the original problem, and therefore some form of inner regularization must be applied. Stopping criteria for the whole process are then based on the regularization of the projected (small) problem. In this paper we consider an ill-posed problem with a noisy right-hand side (observation vector), where the noise level is unknown. We show how the information from the Golub-Kahan iterative bidiagonalization can be used for estimating the noise level. Such information can be useful for constructing efficient stopping criteria in solving ill-posed problems.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/IAA100300802" target="_blank" >IAA100300802: Teorie metod Krylovových podprostorů a její vztah k jiným oblastem matematiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

BIT Numerical Mathematics

ISSN

0006-3835

e-ISSN

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Svazek periodika

49

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

28

Strana od-do

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Kód UT WoS článku

000271948000002

EID výsledku v databázi Scopus

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