Manifold interpolation and model reduction

Research output: Contribution to journalJournal articleResearch

Abstract

One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric structure and thus form so-called matrix manifolds. This work will be featured as a chapter in the upcoming Handbook on Model Order Reduction (P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W.H.A. Schilders, L.M. Silveira, eds, to appear on DE GRUYTER) and reviews the numerical treatment of the most important matrix manifolds that arise in the context of model reduction. Moreover, the principal approaches to data interpolation and Taylor-like extrapolation on matrix manifolds are outlined and complemented by algorithms in pseudo-code.
Original languageEnglish
Journalarxiv.org
Number of pages37
Publication statusPublished - 11. Feb 2019

Bibliographical note

37 pages, 4 figures, featured chapter of upcoming "Handbook on Model Order Reduction", to appear at De Gruyter

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