A parallel algorithm for the eigenvalues and eigenvectors for a general complex matrix

A new parallel Jacobi-like algorithm is developed for computing the eigenvalues of a general complex matrix. Most parallel methods for this parallel typically display only linear convergence. Sequential norm-reducing algorithms also exit and they display quadratic convergence in most cases. The new algorithm is a parallel form of the norm-reducing algorithm due to Eberlein. It is proven that the asymptotic convergence rate of this algorithm is quadratic. Numerical experiments are presented which demonstrate the quadratic convergence of the algorithm and certain situations where the convergence is slow are also identified. The algorithm promises to be very competitive on a variety of parallel architectures

Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization

Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality, convergence speed, and delay. To address these challenges, in this paper, we propose a new algorithmic framework with all these metrics approaching optimality. The salient features of our new algorithm are three-fold: (i) fast convergence: it converges with only $O(\log(1/\epsilon))$ iterations that is the fastest speed among all the existing algorithms; (ii) low delay: it guarantees optimal utility with finite queue length; (iii) simple implementation: the control variables of this algorithm are based on virtual queues that do not require maintaining per-flow information. The new technique builds on a kind of inexact Uzawa method in the Alternating Directional Method of Multiplier, and provides a new theoretical path to prove global and linear convergence rate of such a method without requiring the full rank assumption of the constraint matrix

Structured illumination microscopy for in-vivo human retinal imaging: a theoretical assessment

Structured illumination microscopy applied to in-vivo retinal imaging has the potential to provide a low-cost and powerful diagnostic tool for retinal disease. In this paper the key parameters that affect performance in structured illumination ophthalmoscopy are studied theoretically. These include the number of images that need to be acquired in order to generate a sectioned image, which is affected by the non-stationary nature of the retina during acquisition, the choice of spatial frequency of the illuminating sinusoid, the effect of typical ocular aberrations on axial resolution and the nature of the sinusoidal pattern produced by the illumination system. The results indicate that structured illumination ophthalmoscopy can be a robust technique for achieving axial sectioning in retinal imaging without the need for complex optical systems

The digital simulation of a turbo-charged diesel engine

A mathematical simulation of a six cylinder four stroke water cooled diesel engine is described and then used to study the changes in performance caused by variations of engine paramters and operating conditions. The results are discussed with reference to the mathematical model employed and the physical system. A limited study, to demonstrate the applicability of the simulation, considers the optimisation of a variable geometry system to achieve a performance target

Non-additive Security Games

We have investigated the security game under non-additive utility functions