Manifold interpolation and model reduction

Publikation: Bidrag til tidsskriftTidsskriftartikelForskning

Abstrakt

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.
OriginalsprogEngelsk
Tidsskriftarxiv.org
Antal sider37
StatusUdgivet - 11. feb. 2019

Bibliografisk note

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

Emneord

  • math.NA
  • cs.NA
  • 15-01, 15A16, 15B10, 15B48, 53-04, 65F60, 41-01, 41A05, 65F99, 93A15, 93C30

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