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On Efficiently Updating Singular Value Decomposition Based Reduced Order Models

Zimmermann, Ralf (2011) On Efficiently Updating Singular Value Decomposition Based Reduced Order Models. GAMM Workshop Applied and Numerical Linear Algebra with Special Emphasis on Model Reduction, 22.-23. Sep. 2011, Bremen, Deutschland.

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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 talk, 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 efficient 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/72513/
Document Type:Conference or Workshop Item (Speech)
Title:On Efficiently Updating Singular Value Decomposition Based Reduced Order Models
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Zimmermann, Ralfralf.zimmermann (at) dlr.deUNSPECIFIED
Date:23 September 2011
Refereed publication:No
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Published
Keywords:Singular Value Decomposition, Proper Orthogonal Decomposition, reduced-order model, Eigenspace models, model updating
Event Title:GAMM Workshop Applied and Numerical Linear Algebra with Special Emphasis on Model Reduction
Event Location:Bremen, Deutschland
Event Type:international Conference, Workshop
Event Dates:22.-23. Sep. 2011
Organizer:GAMM Gesellschaft für angewandte Mathematik und Mechanik
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:07 Dec 2011 15:50
Last Modified:31 Jul 2019 19:33

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