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Speeding up Kriging by Using Pivoted Cholesky Decomposition and Low-Rank Structures

Liu, Dishi and Zimmermann, Ralf and Matthies, Hermann G. (2016) Speeding up Kriging by Using Pivoted Cholesky Decomposition and Low-Rank Structures. SIAM Annual Meeting 2016, 11.-15. Jul. 2016, Boston, USA.

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Abstract

Kriging is often impaired in terms of costs and accuracy by ill-conditioned covariance matrices of large dimension N. We propose to tackle both of these problem by using a pivoted Cholesky decomposition (PCD) and a rank-k formulation of Kriging. The PCD solves a rank-deficient but consistent system. By reformulating the maximum likelihood training accordingly, the complexity is reduced to O(k^2N) with k <<N. In numerical tests our approach displays an accuracy comparable to regularization approaches.

Item URL in elib:https://elib.dlr.de/105977/
Document Type:Conference or Workshop Item (Speech)
Title:Speeding up Kriging by Using Pivoted Cholesky Decomposition and Low-Rank Structures
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Liu, Dishidishi.liu (at) dlr.deUNSPECIFIED
Zimmermann, Ralfralf.zimmermann (at) tu-braunschweig.deUNSPECIFIED
Matthies, Hermann G.TU BraunschweigUNSPECIFIED
Date:2016
Refereed publication:No
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Published
Keywords:Kriging, pivoted Cholesky decomposition, aerodynamics, uncertainty, SMARTy, TAU
Event Title:SIAM Annual Meeting 2016
Event Location:Boston, USA
Event Type:international Conference
Event Dates:11.-15. Jul. 2016
Organizer:SIAM
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation and Validation
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering
Deposited By: Görtz, Stefan
Deposited On:27 Sep 2016 08:53
Last Modified:27 Sep 2016 08:53

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