Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information

Ralf Zimmermann

doi:10.1007/978-3-319-39929-4_36

Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information

Ralf Zimmermann

Braunschweig University of Technology

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

A method is proposed for constructing local parametrizations of
orthogonal bases and of subspaces by computing
trajectories in the Stiefel and the Grassmann manifold, respectively.
The trajectories are obtained by exploiting sensitivity information
on the singular value decomposition with respect to parametric changes and
a Taylor-like local linearization suitably adapted to the underlying manifold structure.
An important practical application of the proposed approach is
parametric model reduction (pMOR).
The connection with pMOR is discussed in detail and the results are illustrated by numerical experiment.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications : ENUMATH 2015
Editors	Bulent Karasozen, Murat Manguoğlu, Münevver Tezer-Sezgin, Serdar Göktepe, Ömür Uğur
Volume	112
Publisher	Springer
Publication date	Dec 2016
Pages	379-387
Chapter	V Reduced Order Modeling
ISBN (Print)	978-3-319-39927-0
ISBN (Electronic)	978-3-319-39929-4
DOIs	https://doi.org/10.1007/978-3-319-39929-4_36
Publication status	Published - Dec 2016
Externally published	Yes
Event	European Conference on Numerical Mathematics and Advanced Applications - Middle East Technical University, Ankara, Turkey Duration: 13. Sep 2015 → 18. Sep 2015 http://enumath2015.iam.metu.edu.tr/

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications
Location	Middle East Technical University
Country/Territory	Turkey
City	Ankara
Period	13/09/2015 → 18/09/2015
Internet address	http://enumath2015.iam.metu.edu.tr/

Series	Lecture Notes in Computational Science and Engineering
Volume	112
ISSN	1439-7358

Documents & Links

10.1007/978-3-319-39929-4_36

Cite this

Zimmermann, R. (2016). Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information. In B. Karasozen, M. Manguoğlu, M. Tezer-Sezgin, S. Göktepe, & Ö. Uğur (Eds.), Numerical Mathematics and Advanced Applications: ENUMATH 2015 (Vol. 112, pp. 379-387). Springer. Lecture Notes in Computational Science and Engineering Vol. 112 https://doi.org/10.1007/978-3-319-39929-4_36

Zimmermann, Ralf. / Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information. Numerical Mathematics and Advanced Applications: ENUMATH 2015. editor / Bulent Karasozen ; Murat Manguoğlu ; Münevver Tezer-Sezgin ; Serdar Göktepe ; Ömür Uğur. Vol. 112 Springer, 2016. pp. 379-387 (Lecture Notes in Computational Science and Engineering, Vol. 112).

@inproceedings{e2c753768f9b41e6951c641b0831477c,

title = "Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information",

abstract = "A method is proposed for constructing local parametrizations oforthogonal bases and of subspaces by computingtrajectories in the Stiefel and the Grassmann manifold, respectively.The trajectories are obtained by exploiting sensitivity information on the singular value decomposition with respect to parametric changes anda Taylor-like local linearization suitably adapted to the underlying manifold structure.An important practical application of the proposed approach is parametric model reduction (pMOR).The connection with pMOR is discussed in detail and the results are illustrated by numerical experiment.",

author = "Ralf Zimmermann",

year = "2016",

month = dec,

doi = "10.1007/978-3-319-39929-4_36",

language = "English",

isbn = "978-3-319-39927-0",

volume = "112",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer",

pages = "379--387",

editor = "Bulent Karasozen and Murat Manguoğlu and M{\"u}nevver Tezer-Sezgin and Serdar G{\"o}ktepe and {\"O}m{\"u}r Uğur",

booktitle = "Numerical Mathematics and Advanced Applications",

address = "Germany",

note = "European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015 ; Conference date: 13-09-2015 Through 18-09-2015",

url = "http://enumath2015.iam.metu.edu.tr/",

}

Zimmermann, R 2016, Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information. in B Karasozen, M Manguoğlu, M Tezer-Sezgin, S Göktepe & Ö Uğur (eds), Numerical Mathematics and Advanced Applications: ENUMATH 2015. vol. 112, Springer, Lecture Notes in Computational Science and Engineering, vol. 112, pp. 379-387, European Conference on Numerical Mathematics and Advanced Applications, Ankara, Turkey, 13/09/2015. https://doi.org/10.1007/978-3-319-39929-4_36

Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information. / Zimmermann, Ralf.

Numerical Mathematics and Advanced Applications: ENUMATH 2015. ed. / Bulent Karasozen; Murat Manguoğlu; Münevver Tezer-Sezgin; Serdar Göktepe; Ömür Uğur. Vol. 112 Springer, 2016. p. 379-387 (Lecture Notes in Computational Science and Engineering, Vol. 112).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information

AU - Zimmermann, Ralf

PY - 2016/12

Y1 - 2016/12

N2 - A method is proposed for constructing local parametrizations oforthogonal bases and of subspaces by computingtrajectories in the Stiefel and the Grassmann manifold, respectively.The trajectories are obtained by exploiting sensitivity information on the singular value decomposition with respect to parametric changes anda Taylor-like local linearization suitably adapted to the underlying manifold structure.An important practical application of the proposed approach is parametric model reduction (pMOR).The connection with pMOR is discussed in detail and the results are illustrated by numerical experiment.

AB - A method is proposed for constructing local parametrizations oforthogonal bases and of subspaces by computingtrajectories in the Stiefel and the Grassmann manifold, respectively.The trajectories are obtained by exploiting sensitivity information on the singular value decomposition with respect to parametric changes anda Taylor-like local linearization suitably adapted to the underlying manifold structure.An important practical application of the proposed approach is parametric model reduction (pMOR).The connection with pMOR is discussed in detail and the results are illustrated by numerical experiment.

U2 - 10.1007/978-3-319-39929-4_36

DO - 10.1007/978-3-319-39929-4_36

M3 - Article in proceedings

SN - 978-3-319-39927-0

VL - 112

T3 - Lecture Notes in Computational Science and Engineering

SP - 379

EP - 387

BT - Numerical Mathematics and Advanced Applications

A2 - Karasozen, Bulent

A2 - Manguoğlu, Murat

A2 - Tezer-Sezgin, Münevver

A2 - Göktepe, Serdar

A2 - Uğur, Ömür

PB - Springer

T2 - European Conference on Numerical Mathematics and Advanced Applications

Y2 - 13 September 2015 through 18 September 2015

ER -

Zimmermann R. Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information. In Karasozen B, Manguoğlu M, Tezer-Sezgin M, Göktepe S, Uğur Ö, editors, Numerical Mathematics and Advanced Applications: ENUMATH 2015. Vol. 112. Springer. 2016. p. 379-387. (Lecture Notes in Computational Science and Engineering, Vol. 112). doi: 10.1007/978-3-319-39929-4_36

Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information

Abstract

Conference

Documents & Links

Fingerprint

Cite this