Algebraic properties of projected problems in LSQR
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10468210" target="_blank" >RIV/00216208:11320/23:10468210 - isvavai.cz</a>
Výsledek na webu
<a href="https://onlinelibrary.wiley.com/doi/10.1002/pamm.202300161" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1002/pamm.202300161</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/pamm.202300161" target="_blank" >10.1002/pamm.202300161</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Algebraic properties of projected problems in LSQR
Popis výsledku v původním jazyce
LSQR represents a standard Krylov projection method for the solution of systems of linear algebraic equations, linear approximation problems or regularization of discrete inverse problem. Its convergence properties (residual norms, error norms, influence of finite precision arithmetic etc.) have been widely studied. It has been observed that the components of the solution of the projected bidiagonal problem typically increase and their sign alternates. This behavior is the core of approximation properties of LSQR and is observed also for hybrid LSQR with inner Tikhonov regularization. Here we provide rigorous analysis of sign changes and monotonicity of individual components of projected solutions and projected residuals in LSQR. The results hold also for Hybrid LSQR with a fixed inner regularization parameter. The derivations do not rely on maintaining orthogonality in Krylov bases determined by the bidiagonalization process. Numerical illustration is included.
Název v anglickém jazyce
Algebraic properties of projected problems in LSQR
Popis výsledku anglicky
LSQR represents a standard Krylov projection method for the solution of systems of linear algebraic equations, linear approximation problems or regularization of discrete inverse problem. Its convergence properties (residual norms, error norms, influence of finite precision arithmetic etc.) have been widely studied. It has been observed that the components of the solution of the projected bidiagonal problem typically increase and their sign alternates. This behavior is the core of approximation properties of LSQR and is observed also for hybrid LSQR with inner Tikhonov regularization. Here we provide rigorous analysis of sign changes and monotonicity of individual components of projected solutions and projected residuals in LSQR. The results hold also for Hybrid LSQR with a fixed inner regularization parameter. The derivations do not rely on maintaining orthogonality in Krylov bases determined by the bidiagonalization process. Numerical illustration is included.
Klasifikace
Druh
D - Stať ve sborníku
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název statě ve sborníku
Proceedings in Applied Mathematics and Mechanics
ISBN
—
ISSN
1617-7061
e-ISSN
—
Počet stran výsledku
6
Strana od-do
—
Název nakladatele
John Wiley & Sons, Inc.
Místo vydání
Weinheim
Místo konání akce
Drážďany, Německo
Datum konání akce
30. 5. 2023
Typ akce podle státní příslušnosti
EUR - Evropská akce
Kód UT WoS článku
—