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Fall; 2010 Stochastic alternating projections
Persi Diaconis, Kshitij Khare, Laurent Saloff-Coste
Illinois J. Math. 54(3): 963-979 (Fall; 2010). DOI: 10.1215/ijm/1336568522

Abstract

We show how basic work of Don Burkholder on iterated conditional expectations is intimately connected to a standard tool of scientific computing—Glauber dynamics (also known as the Gibbs sampler). We begin with von Neumann’s alternating projection theorem using an example of Burkholder’s. We then review Burkholder’s theorem. Finally, we introduce Glauber dynamics and show how Burkholder’s theorem can be harnessed to prove convergence. In the other direction, we show how classical convergence rates involving the angle between subspaces can be substantially refined in several cases.

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Persi Diaconis. Kshitij Khare. Laurent Saloff-Coste. "Stochastic alternating projections." Illinois J. Math. 54 (3) 963 - 979, Fall; 2010. https://doi.org/10.1215/ijm/1336568522

Information

Published: Fall; 2010
First available in Project Euclid: 9 May 2012

zbMATH: 1268.60098
MathSciNet: MR2928343
Digital Object Identifier: 10.1215/ijm/1336568522

Subjects:
Primary: 46N30, 60J10
Secondary: 60J27, 65C40

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 3 • Fall; 2010
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