A Fast Newton's Algorithm for Entropy Maximization in Phase Determination

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dc.contributor.authorWu, Zhijunen_US
dc.contributor.authorPhillips, Georgeen_US
dc.contributor.authorTapia, Richarden_US
dc.contributor.authorZhang, Yinen_US
dc.date.accessioned2018-06-18T17:47:33Zen_US
dc.date.available2018-06-18T17:47:33Zen_US
dc.date.issued1999-05en_US
dc.date.noteMay 1999 (Revised July 2000)en_US
dc.description.abstractA long-standing problem in X-ray crystallography, known as the phase problem, is to determine the phases for a large set of complex variables, called the structure factors of the crystal, given their magnitudes obtained from X-ray diffraction experiments. We introduce a statistical phase estimation approach to the problem. This approach requires solving a special class of entropy maximization problems repeatedly to obtain the joint probability distribution of the structure factors. The entropy maximization problem is a semi-infinite convex program, which can be solved in a finite dual space by using a standard Newton's method. The Newton's method converges quadratically, but is costly in general, requiring O(n log n) floating point operations in every iteration, where n is the number of variables. We present a fast Newton's algorithm for solving the entropy maximization problem. The algorithm requires only O(n log n) floating point operations for each of its iterates, yet has the same convergence rate as the standard Newton. We describe the algorithm and discuss related computational issues. Numerical results on simple test cases will also be presented to demonstrate the behavior of the algorithm.en_US
dc.format.extent30 ppen_US
dc.identifier.citationWu, Zhijun, Phillips, George, Tapia, Richard, et al.. "A Fast Newton's Algorithm for Entropy Maximization in Phase Determination." (1999) <a href="https://hdl.handle.net/1911/101919">https://hdl.handle.net/1911/101919</a>.en_US
dc.identifier.digitalTR99-14en_US
dc.identifier.urihttps://hdl.handle.net/1911/101919en_US
dc.language.isoengen_US
dc.titleA Fast Newton's Algorithm for Entropy Maximization in Phase Determinationen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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