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A Comprehensive Comparison of Various Algorithms for Efficiently Updating Singular Value Decomposition Based Reduced Order Models

Zimmermann, Ralf (2011) A Comprehensive Comparison of Various Algorithms for Efficiently Updating Singular Value Decomposition Based Reduced Order Models. DLR-Interner Bericht. DLR-IB 124-2011/3, 19 S. DLR.

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Abstract

Efficiently updating an SVD-based data representation while keeping accurate track of the data mean when new observations are coming in is a common objective in many practical application scenarios. In this paper, two different SVD update algorithms capable of treating an arbitrary number of new observations are introduced following the symmetric EVD philosophy. These methods are compared to an SVD update method known from the literature. The comparison criterion of interest is the theoretical computational complexity, it being understood that the dimension of the observation vectors is much larger than the number of observations. From this point of view, a hierarchy of methods is derived, and the computational savings of the update strategies pursuing the symmetric EVD approach are demonstrated. It is exposed, how the compression level of the initial SVD model affects the performance of these algorithms and the break point where one method becomes more efficent than the other is determined. In addition, simple rules of thumb are derived for easing the choice of an algorithm valid in most practical scenarios.

Item URL in elib:https://elib.dlr.de/70251/
Document Type:Monograph (DLR-Interner Bericht)
Title:A Comprehensive Comparison of Various Algorithms for Efficiently Updating Singular Value Decomposition Based Reduced Order Models
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Zimmermann, Ralfralf.zimmermann (at) dlr.deUNSPECIFIED
Date:June 2011
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Number of Pages:19
Publisher:DLR
Series Name:DLR-Interner Bericht
ISSN:1614-7790
Status:Published
Keywords:proper orthogonal decomposition, reduced-order model, Eigenspace models, principal component analysis, SVD updating
Institution:DLR Braunschweig
Department:Institute of Aerodynamics and Flow Technology
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research (old)
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation & Validation (old)
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > CASE
Deposited By: Zimmermann, Dr. Ralf
Deposited On:05 Aug 2011 12:08
Last Modified:31 Jul 2019 19:32

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