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Biorthogonal decomposition: Difference between revisions
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The Biorthogonal Decomposition (BOD, also known as Proper Orthogonal Decomposition, POD<ref>P. Holmes, J.L. Lumley, and G. Berkooz, ''Turbulence, Coherent Structures, Dynamical Systems and Symmetry'', Cambridge University Press (1996) ISBN 0521634199</ref>) applies to the analysis of multipoint measurements | The Biorthogonal Decomposition (BOD, also known as Proper Orthogonal Decomposition, POD<ref>P. Holmes, J.L. Lumley, and G. Berkooz, ''Turbulence, Coherent Structures, Dynamical Systems and Symmetry'', Cambridge University Press (1996) {{ISBN|0521634199}}</ref>) applies to the analysis of multipoint measurements | ||
:<math>Y(i,j)\,</math> | :<math>Y(i,j)\,</math> | ||
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Thus, the oscillations of the spatiotemporal fluctuating field are represented by means of a very small number of spatio-temporal modes that are constructed from the data themselves, without prejudice regarding the mode shape. | Thus, the oscillations of the spatiotemporal fluctuating field are represented by means of a very small number of spatio-temporal modes that are constructed from the data themselves, without prejudice regarding the mode shape. | ||
<ref>T. Dudok de Wit et al., ''The biorthogonal decomposition as a tool for investigating fluctuations in plasmas'', [ | <ref>T. Dudok de Wit et al., ''The biorthogonal decomposition as a tool for investigating fluctuations in plasmas'', [[doi:10.1063/1.870481| Phys. Plasmas '''1''' (1994) 3288]]</ref> | ||
A limitation of the technique is that it assumes space-time separability. | A limitation of the technique is that it assumes space-time separability. | ||