A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction

Simple item page
dc.contributor.authorChaturantabut, Saifonen_US
dc.contributor.authorSorensen, Danny C.en_US
dc.date.accessioned2018-06-19T17:46:08Zen_US
dc.date.available2018-06-19T17:46:08Zen_US
dc.date.issued2010-12en_US
dc.date.noteDecember 2010en_US
dc.description.abstractThis paper derives state space error bounds for the solutions of reduced systems constructed using Proper Orthogonal Decomposition (POD) together with the Discrete Empirical Interpolation Method (DEIM) recently developed in [S. Chaturantabut and D.C. Sorensen, SISC 2010, pp. 2737-2764 ] for nonlinear dynamical systems. The resulting error bounds are shown to be proportional to the sums of the singular values corresponding to neglected POD basis vectors both in Galerkin projection of the reduced system and in the DEIM approximation of the nonlinear term. The analysis is particularly relevant to ODE systems arising from spatial discretizations of parabolic PDEs. The derivation clearly identifies where the parabolicity is crucial. It also shows exactly how the DEIM approximation error involving the nonlinear term comes into play.en_US
dc.format.extent17 ppen_US
dc.identifier.citationChaturantabut, Saifon and Sorensen, Danny C.. "A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction." (2010) <a href="https://hdl.handle.net/1911/102173">https://hdl.handle.net/1911/102173</a>.en_US
dc.identifier.digitalTR10-32en_US
dc.identifier.urihttps://hdl.handle.net/1911/102173en_US
dc.language.isoengen_US
dc.relation.HasVersionS. Chaturantabut and D.C. Sorensen, Nonlinear model reduction via discrete empirical interpolation, SIAM Journal on Scientific Computing, 32 (2010), pp. 2737-2764en_US
dc.titleA State Space Error Estimate for POD-DEIM Nonlinear Model Reductionen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
TR10-32.pdf
Size:
364.84 KB
Format:
Adobe Portable Document Format
Download
Collections
CMOR Technical Reports