For arbitrary real matrices F and G, the positive semi-deenite Procrustes problem is minimization of the Frr obenius norm of F ? PG with respect to positive semi-deenite symmetric P. Existing solution algorithms are based on a convex programming approach. Here an unconstrained non-convex approach is taken, namely writing P = E 0 E and optimizing with respect to E. The main result is that all lo...

We present LHIP, a system for incremental grammar development using an extended DCG formalism. The system uses a robust island-based parsing method controlled by user-defined performance thresholds.

In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.

This note outlines an algorithm for solving the complex “matrix Procrustes problem”. This is a least-squares approximation over the cone of positive semi-definite Hermitian matrices, which has a number of applications in the areas of Optimization, Signal Processing and Control. The work generalises the method of [J.C. Allwright, “Positive semidefinite matrices: Characterization via conical hull...

We look at the real positive (semi)definite matrix completion problem from the relative entropy minimization viewpoint. After the problem is transformed into the standard maxdet from, conditions are sought for existence of positive (semi)definite completions. Using basic tools of convex analysis results previously established using graph-theoretic or functional-analytic techniques are recovered...

The use of Frege-Russell style definite descriptions for giving meaning to functions has been long established and we investigate their use in the development of Functional Programs and from these to the development of correct imperative programs. In particular, we investigate the development of a functional program for a problem, "Odd powers of odd integers", discussed by Dijsktra. If the corr...

Semi-definite rank minimization problems model a wide range of applications in both signal processing and machine learning fields. This class of problem is NP-hard in general. In this paper, we propose a proximal Alternating Direction Method (ADM) for the well-known semi-definite rank regularized minimization problem. Specifically, we first reformulate this NP-hard problem as an equivalent bico...

We consider the problem of minimizing the spectral condition number of a positive definite matrix by completion: min{cond( [ A BH B X ] ) : [ A BH B X ] positive definite}, where A is an n × n Hermitian positive definite matrix, B a p × n matrix and X is a free p× p Hermitian matrix. We reduce this problem to an optimization problem for a convex function in one variable. Using the minimal solut...