Commun. Comput. Phys., 12 (2012), pp. 1520-1540.


System Reduction Using an LQR-Inspired Version of Optimal Replacement Variables

Alex Solomonoff 1*

1 Camberville Research Institute, Somerville, MA, USA; and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.

Received 19 March 2011; Accepted (in revised version) 27 January 2012
Available online 4 June 2012
doi:10.4208/cicp.190311.270112a

Abstract

Optimal Replacement Variables (ORV) is a method for approximating a large system of ODEs by one with fewer equations, while attempting to preserve the essential dynamics of a reduced set of variables of interest. An earlier version of ORV [1] had some issues, including limited accuracy and in some rare cases, instability. Here we present a new version of ORV, inspired by the linear quadratic regulator problem of control theory, which provides better accuracy, a guarantee of stability and is in some ways easier to use.

AMS subject classifications: 65M06, 65M30, 65M70

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Key words: System reduction, optimal replacement variables, resolved variables, optimal prediction.

*Corresponding author.
Email: alex.solomonoff@yahoo.com (A. Solomonoff)
 

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