Optimality of Balanced Proper Orthogonal Decomposition for Data Reconstruction II: Further Approximation Results

Abstract

In our earlier paper Singler (2010), we showed two separate data sets can be optimally approximated using balanced proper orthogonal decomposition (POD) modes derived from the data. In this work, we prove new results concerning the approximation capability of the balanced POD modes. We give exact computable expressions for the errors between the individual data sets and the low order balanced POD data reconstructions. We also consider approximating elements of the Hilbert space using various projections onto the balanced POD modes. We discuss the relevance of these results to balanced POD model reduction of nonlinear partial differential equations.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Balanced Proper Orthogonal Decomposition; Data Approximation; Hilbert-Schmidt Operators; Proper Orthogonal Decomposition

International Standard Serial Number (ISSN)

0022-247X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 Elsevier, All rights reserved.

Publication Date

01 Jan 2015

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