Solving large linear least squares problems with linear equality constraints

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455908" target="_blank" >RIV/00216208:11320/22:10455908 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xd3yR9sEn7" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xd3yR9sEn7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10543-022-00930-2" target="_blank" >10.1007/s10543-022-00930-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Solving large linear least squares problems with linear equality constraints

Popis výsledku v původním jazyce

We consider the problem of solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly.While some classical approaches are theoretically well founded, they can face difficultieswhen thematrix ofconstraints contains dense rows or if an algorithmic transformation used in the solution process results in a modified problem that is much denser than the original one. We propose modifications with an emphasis on requiring that the constraints be satisfiedwith a small residual.We examine combining the null-space method with our recently developed algorithm for computing a null-space basis matrix for a &quot;wide&quot; matrix.We further show that a direct elimination approach enhanced by careful pivoting can be effective in transforming the problem to an unconstrained sparse-dense least squares problem that can be solved with existing direct or iterative methods. We also present a number of solution variants that employ an augmented system formulation, which can be attractive for solving a sequence of related problems. Numerical experiments on problems coming from practical applications are used throughout to demonstrate the effectiveness of the different approaches.

Název v anglickém jazyce

Solving large linear least squares problems with linear equality constraints

Popis výsledku anglicky

We consider the problem of solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly.While some classical approaches are theoretically well founded, they can face difficultieswhen thematrix ofconstraints contains dense rows or if an algorithmic transformation used in the solution process results in a modified problem that is much denser than the original one. We propose modifications with an emphasis on requiring that the constraints be satisfiedwith a small residual.We examine combining the null-space method with our recently developed algorithm for computing a null-space basis matrix for a &quot;wide&quot; matrix.We further show that a direct elimination approach enhanced by careful pivoting can be effective in transforming the problem to an unconstrained sparse-dense least squares problem that can be solved with existing direct or iterative methods. We also present a number of solution variants that employ an augmented system formulation, which can be attractive for solving a sequence of related problems. Numerical experiments on problems coming from practical applications are used throughout to demonstrate the effectiveness of the different approaches.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

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

1572-9125

Svazek periodika

62

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

1765-1787

Kód UT WoS článku

000821978300002

EID výsledku v databázi Scopus

2-s2.0-85133412705