CRPC-TR99792						May 1999

Title: An Efficient Newton's Method for Entropy Maximization in Phase 
Determination

Authors: Zhijun Wu, George Phillips, Richard Tapia, and Yin Zhang

Submitted November 1999

Abstract: 
The joint probability distribution is required for every basis set of
structure factors in the Bayesian statistical approach to phase
determination. It is computed by maximizing the entropy of the crystal
system subject to certain constraints on the structure factors. We propose
a Newton's method for the entropy maximization problem. In particular, we
show that for m structure factors the method requires only O (m log m)
floating point operations when the problem structure is exploited. The
background of the Bayesian statistical approach to phase determination is
introduced. The entropy maximization problem and related solution methods
are described. The proposed Newton's method is presented along with its
convergence and complexity properties.

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Zhijun Wu
zwu@caam.rice.edu
Department of Biochemistry and Cell Biology
Rice University

George Phillips
georgep@rice.edu
Department of Computational and Applied Mathematics
Rice University

Richard Tapia
rat@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University

Yin Zhang
zhang@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University