Observations on the Proper Orthogonal DecompositionThe Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L(2) 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.
Document ID
19940035735
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Berkooz, Gal (Cornell Univ. Ithaca, NY, United States)
Date Acquired
August 16, 2013
Publication Date
January 1, 1992
Publication Information
Publication: In: Studies in turbulence (A94-12376 02-34)