KRYLOV SUBSPACE APPROACH TO CORE PROBLEMS WITHIN MULTILINEAR APPROXIMATION PROBLEMS: A UNIFYING FRAMEWORK

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10468019" target="_blank" >RIV/00216208:11320/23:10468019 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/46747885:24510/23:00010098

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DeO.DwwZ3G" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DeO.DwwZ3G</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/21M1462155" target="_blank" >10.1137/21M1462155</a>

Jazyk výsledku

angličtina

Název v původním jazyce

KRYLOV SUBSPACE APPROACH TO CORE PROBLEMS WITHIN MULTILINEAR APPROXIMATION PROBLEMS: A UNIFYING FRAMEWORK

Popis výsledku v původním jazyce

Error contaminated linear approximation problems appear in a large variety of applications. The presence of redundant or irrelevant data complicates their solution. It was shown that such data can be removed by the core reduction yielding a minimally dimensioned subproblem called the core problem. Direct (SVD or Tucker decomposion-based) reduction has been introduced previously for problems with matrix models and vector, or matrix, or tensor observations; and also for problems with bilinear models. For the cases of vector and matrix observations a Krylov subspace method, the generalized Golub--Kahan bidiagonalization, can be used to extract the core problem. In this paper, we first unify previously studied variants of linear approximation problems under the general framework of a multilinear approximation problem. We show how the direct core reduction can be extended to it. Then we show that the generalized Golub--Kahan bidiagonalization yields the core problem for any multilinear approximation problem. This further allows one to prove various properties of core problems, in particular, we give upper bounds on the multiplicity of singular values of reduced matrices.

Název v anglickém jazyce

KRYLOV SUBSPACE APPROACH TO CORE PROBLEMS WITHIN MULTILINEAR APPROXIMATION PROBLEMS: A UNIFYING FRAMEWORK

Popis výsledku anglicky

Error contaminated linear approximation problems appear in a large variety of applications. The presence of redundant or irrelevant data complicates their solution. It was shown that such data can be removed by the core reduction yielding a minimally dimensioned subproblem called the core problem. Direct (SVD or Tucker decomposion-based) reduction has been introduced previously for problems with matrix models and vector, or matrix, or tensor observations; and also for problems with bilinear models. For the cases of vector and matrix observations a Krylov subspace method, the generalized Golub--Kahan bidiagonalization, can be used to extract the core problem. In this paper, we first unify previously studied variants of linear approximation problems under the general framework of a multilinear approximation problem. We show how the direct core reduction can be extended to it. Then we show that the generalized Golub--Kahan bidiagonalization yields the core problem for any multilinear approximation problem. This further allows one to prove various properties of core problems, in particular, we give upper bounds on the multiplicity of singular values of reduced matrices.

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

2023

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Matrix Analysis and Applications

ISSN

0895-4798

e-ISSN

1095-7162

Svazek periodika

44

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

53-79

Kód UT WoS článku

000974412700001

EID výsledku v databázi Scopus

2-s2.0-85151047636