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Observations on the Proper Orthogonal Decomposition

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Studies in Turbulence

Abstract

The Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L2 optimal sense. It is used in diverse disciplines from image processing to turbulence. Recently the P.O.D. is receiving much attention as a tool for studying dynamics of systems in infinite dimensional space. This paper reviews the mathematical fundamentals of this theory. Also included are results on the span of the eigenfunction basis, a geometric corollary due to Chebyshev’s inequality and a relation between the P.O.D. symmetry and ergodicity.

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Author information

Authors and Affiliations

  1. Cornell University, Ithaca, NY, USA, 14853

    Gal Berkooz

  2. Center for Applied Math, 305 Sage Hall Cornell University, 14853, Ithaca, NY, USA

    Gal Berkooz

Authors
  1. Gal Berkooz
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Editor information

Editors and Affiliations

  1. Theoretical Flow Physics Branch, NASA Langley Research Center, 23665-5225, Hampton, Virginia, USA

    Thomas B. Gatski

  2. ICASE, NASA Langley Research Center, 23665-5225, Hampton, Virginia, USA

    Charles G. Speziale  & Sutanu Sarkar  & 

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© 1992 Springer-Verlag New York, Inc.

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Berkooz, G. (1992). Observations on the Proper Orthogonal Decomposition. In: Gatski, T.B., Speziale, C.G., Sarkar, S. (eds) Studies in Turbulence. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2792-2_16

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  • DOI: https://doi.org/10.1007/978-1-4612-2792-2_16

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7672-2

  • Online ISBN: 978-1-4612-2792-2

  • eBook Packages: Springer Book Archive

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