The 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.
CITATION STYLE
Berkooz, G. (1992). Observations on the Proper Orthogonal Decomposition. In Studies in Turbulence (pp. 229–247). Springer New York. https://doi.org/10.1007/978-1-4612-2792-2_16
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