Title

A Note on Incremental POD Algorithms for Continuous Time Data

Abstract

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

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

International Standard Serial Number (ISSN)

0168-9274

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 IMACS, All rights reserved.

Publication Date

01 Oct 2019

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