A Note on Incremental POD Algorithms for Continuous Time Data


In our earlier work Fareed et al. (2018) [18], we developed an incremental approach to compute the proper orthogonal decomposition (POD) of PDE simulation data. Specifically, we developed an incremental algorithm for the SVD with respect to a weighted inner product for the discrete time POD computations. For continuous time data, we used an approximate approach to arrive at a discrete time POD problem and then applied the incremental SVD algorithm. In this note, we analyze the continuous time case with simulation data that is piecewise constant in time such that each data snapshot is expanded in a finite collection of basis elements of a Hilbert space. We first show that the POD is determined by the SVD of two different data matrices with respect to weighted inner products. Next, we develop incremental algorithms for approximating the two matrix SVDs with respect to the different weighted inner products. Finally, we show neither approximate SVD is more accurate than the other; specifically, we show the incremental algorithms return equivalent results.


Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Continuous time; Incremental SVD; Proper orthogonal decomposition; Weighted inner products

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


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Publication Date

01 Oct 2019