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

Result code in 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>

Alternative codes found

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

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/IAA100300802" target="_blank" >IAA100300802: Theory of Krylov subspace methods and its relationship to other mathematical disciplines</a><br>

Continuities

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

Publication year

2009

Confidentiality

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

Name of the periodical

BIT Numerical Mathematics

ISSN

0006-3835

e-ISSN

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Volume of the periodical

49

Issue of the periodical within the volume

4

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

28

Pages from-to

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UT code for WoS article

000271948000002

EID of the result in the Scopus database

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