Noise Representation in Residuals of LSQR, LSMR, and CRAIG Regularization

Kód výsledku v IS VaVaI

RIV/67985807:_____/17:00477277 - isvavai.cz

Nalezeny alternativní kódy

RIV/00216208:11320/17:10362681 RIV/46747885:24510/17:00004896

Výsledek na webu

http://dx.doi.org/10.1016/j.laa.2017.07.031

DOI - Digital Object Identifier

10.1016/j.laa.2017.07.031

Jazyk výsledku

angličtina

Název v původním jazyce

Noise Representation in Residuals of LSQR, LSMR, and CRAIG Regularization

Popis výsledku v původním jazyce

Golub-Kahan iterative bidiagonalization represents the core algorithm in several regularization methods for solving large linear noise-polluted ill-posed problems. We consider a general noise setting and derive explicit relations between (noise contaminated) bidiagonalization vectors and the residuals of bidiagonalization-based regularization methods LSQR, LSMR, and CRAIG. For LSQR and LSMR residuals we prove that the coefficients of the linear combination of the computed bidiagonalization vectors reflect the amount of propagated noise in each of these vectors. For CRAIG the residual is only a multiple of a particular bidiagonalization vector. We show how its size indicates the regularization effect in each iteration by expressing the CRAIG solution as the exact solution to a modified compatible problem. Validity of the results for larger two-dimensional problems and influence of the loss of orthogonality is also discussed.

Název v anglickém jazyce

Noise Representation in Residuals of LSQR, LSMR, and CRAIG Regularization

Popis výsledku anglicky

Golub-Kahan iterative bidiagonalization represents the core algorithm in several regularization methods for solving large linear noise-polluted ill-posed problems. We consider a general noise setting and derive explicit relations between (noise contaminated) bidiagonalization vectors and the residuals of bidiagonalization-based regularization methods LSQR, LSMR, and CRAIG. For LSQR and LSMR residuals we prove that the coefficients of the linear combination of the computed bidiagonalization vectors reflect the amount of propagated noise in each of these vectors. For CRAIG the residual is only a multiple of a particular bidiagonalization vector. We show how its size indicates the regularization effect in each iteration by expressing the CRAIG solution as the exact solution to a modified compatible problem. Validity of the results for larger two-dimensional problems and influence of the loss of orthogonality is also discussed.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

GC17-04150J: Robustní dvojúrovňové simulace založené na Fourierově metodě a metodě konečných prvků: Odhady chyb, redukované modely a stochastika

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

—

Svazek periodika

533

Číslo periodika v rámci svazku

15

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

357-379

Kód UT WoS článku

000412965500017

EID výsledku v databázi Scopus

2-s2.0-85026866916