## Search

Now showing items 41-50 of 67

#### The Bayesian Statistical Approach to the Phase Problem in Protein X-ray Crystallography

(1999-04)

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

(1999-05)

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

(1999-04)

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 ...

#### Properties of A Class of Preconditioners for Weighted Least Squares Problems

(1999-04)

A sequence of weighted linear least squares problems arises from interior-point methods for linear programming where the changes from one problem to the next are the weights and the right hand side. One approach for solving ...

#### On Convergence of Minimization Methods: Attraction, Repulsion and Selection

(1999-03)

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 ...

#### Solving a Low-Rank Factorization Model for Matrix Completion by a Non-linear Successive Over-Relaxation Algorithm

(2010-03)

The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclear-norm minimization which requires computing singular value ...

#### Trace-Penalty Minimization for Large-scale Eigenspace Computation

(2013-02)

The Rayleigh-Ritz (RR) procedure, including orthogonalization, constitutes a major bottleneck in computing relatively high-dimensional eigenspaces of large sparse matrices. Although operations involved in RR steps can be ...

#### An Alternating Direction and Projection Algorithm for Structure-enforced Matrix Factorization

(2013-10)

Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models ap- pearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning ...

#### Maximum Stable Set Formulations and Heuristics Based on Continuous Optimization

(2000-12)

The stability number for a given graph G is the size of a maximum stable set in G. The Lovasz theta number provides an upper bound on the stability number and can be computed as the optimal value of the Lovasz semidefinite ...

#### Rank-Two Relaxation Heuristics for Max-Cut and Other Binary Quadratic Programs

(2000-11)

Semidefinite relaxation for certain discrete optimization problems involves replacing a vector-valued variable by a matrix-valued one, producing a convex program while increasing the number of variables by an order of ...