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A fast Newton method for entropy maximization in statistical phase estimation.

Z Wu¹, G N Phillips, R Tapia

¹Department of Mathematics, Iowa State University, Ames, IA 50010, USA. zhijun@iastate.edu

Acta Crystallographica. Section A, Foundations of Crystallography

|October 27, 2001

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A new, faster Newton method significantly reduces computational cost for Bayesian phase estimation. This approach achieves O(n log n) operations per iteration, improving efficiency without sacrificing convergence speed.

Area of Science:

Statistical physics
Computational mathematics
Bayesian inference

Background:

Phase estimation is crucial in various scientific fields.
Traditional Newton methods for entropy maximization are computationally intensive (O(n^3)).
Bayesian statistical approaches offer a robust framework for phase estimation.

Purpose of the Study:

To introduce a computationally efficient Newton method for Bayesian phase estimation.
To reduce the complexity of solving entropy maximization problems.
To maintain the convergence rate of standard Newton methods.

Main Methods:

Development of a fast Newton method tailored for entropy maximization.
Analysis of computational complexity, achieving O(n log n) operations per iteration.

Related Experiment Videos

Implementation and testing on simple phase estimation scenarios.

Main Results:

The proposed method demonstrates a substantial reduction in computational cost compared to standard O(n^3) methods.
The fast Newton method exhibits comparable convergence rates to the standard approach.
Numerical results validate the method's effectiveness and behavior.

Conclusions:

The fast Newton method provides a significant computational advantage for Bayesian phase estimation.
This advancement enables more efficient analysis in applications requiring phase estimation.
The method is practical and validated through numerical examples.