On the optimality of the proper orthogonal decomposition and balanced truncation

Abstract

The proper orthogonal decomposition (POD), also known as Karhunen-Loeve decomposition or principal component analysis, and balanced truncation, are shown to be optimal in the sense of distance minimizations in spaces of Hilbert-Schmidt or trace-class 2 integral operators. Both POD and balanced truncation are shown to be optimal approximations by finite rank… (More)
DOI: 10.1109/CDC.2008.4739458

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