Optimality of Balanced Proper Orthogonal Decomposition for Data Reconstruction

Abstract

Proper orthogonal decomposition (POD) finds an orthonormal basis yielding an optimal reconstruction of a given dataset. We consider an optimal data reconstruction problem for two general datasets related to balanced POD, which is an algorithm for balanced truncation model reduction for linear systems. We consider balanced POD outside of the linear systems framework, and prove that it solves the optimal data reconstruction problem. The theoretical result is illustrated with an example.

Keywords:

• Balanced proper orthogonal composition
• Data approximation
• Hilbert–Schmidt operators
• Proper orthogonal decomposition

AMS Subject Classification:

• Primary 41
• Secondary 47B10

ACKNOWLEDGMENT

This work was supported in part by a grant from the University of Missouri Research Board.