Now showing items 1-5 of 5
The Bayesian Statistical Approach to the Phase Problem in Protein X-ray Crystallography
We review a Bayesian statistical approach to the phase problem in protein X-ray crystallography. We discuss the mathematical foundations and the computational issues. The introduction to the theory and the algorithms does ...
A Fast Newton's Algorithm for Entropy Maximization in Phase Determination
A 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 ...
The Sphere of Convergence of Newton's Method on Two Equivalent Systems from Nonlinear Programming
We study a local feature of a Newton logarithmic barrier function method and a Newton primal-dual interior-point method. In particular, we study the radius of the sphere of convergence of Newton's method on two equivalent ...
On Convergence of Minimization Methods: Attraction, Repulsion and Selection
In this paper, we introduce a rather straightforward but fundamental observation concerning the convergence of the general iteration process. x^(k+1) = x^k - alpha(x^k) [B(x^k)]^(-1) gradf(x^k) for minimizing a function ...
Selective Search for Global Optimization of Zero or Small Residual Least-Squares Problems: A Numerical Study
In this paper, we consider searching for global minima of zero or small residual, nonlinear least-squares problems. We propose a selective search approach based on the concept of selective minimization recently introduced ...