The Bordering Algorithm and Path Following Near Singular Points of Higher Nullity

We study the behavior of the bordering algorithm (a form of block elimination) for solving nonsingular linear systems with coefficient matrices in the partitioned form (A & B \\ C^* & D) when N(A)≧1. Systems with this structure naturally occur in path following procedures. We show that under appropriate assumptions, the algorithm, which is based on solving systems with coefficient matrix A, works as A varies along a path and goes through singular points. The required assumptions are justified for a large class of problems coming from discretizations of boundary value problems for differential equations

Accurate difference methods for linear ordinary differential systems subject to linear constraints

We consider the general system of n first order linear ordinary differential equations y'(t)=A(t)y(t)+g(t), a<t< b, subject to "boundary" conditions, or rather linear constraints, of the form Σ^(N)_(ν=1) B_(ν)y(τ_ν)=β Here y(t), g(t) and II are n-vectors and A(t), Bx,..., BN are n × n matrices. The N distinct points {τ_ν} lie in [a,b] and we only require N ≧ 1. Thus as special cases initial value problems, N=1, are included as well as the general 2-point boundary value problem, N=2, with τ_1=a, τ_2=b. (More general linear constraints are also studied, see (5.1) and (5.17).

Automatic speech recognition in air-ground data link

In the present air traffic system, information presented to the transport aircraft cockpit crew may originate from a variety of sources and may be presented to the crew in visual or aural form, either through cockpit instrument displays or, most often, through voice communication. Voice radio communications are the most error prone method for air-ground data link. Voice messages can be misstated or misunderstood and radio frequency congestion can delay or obscure important messages. To prevent proliferation, a multiplexed data link display can be designed to present information from multiple data link sources on a shared cockpit display unit (CDU) or multi-function display (MFD) or some future combination of flight management and data link information. An aural data link which incorporates an automatic speech recognition (ASR) system for crew response offers several advantages over visual displays. The possibility of applying ASR to the air-ground data link was investigated. The first step was to review current efforts in ASR applications in the cockpit and in air traffic control and evaluated their possible data line application. Next, a series of preliminary research questions is to be developed for possible future collaboration