Past

Taking a view common in the finite element analysis, we interpret

the first N terms of the usual Fourier series solution as the exact

solution of an approximating problem in a subspace spanned by the

eigenfunctions of the underlying Sturm Liouville problem. This view

leads to a consistent solution technique for the heat, wave and

Poisson's equation, and allows an analysis of the error caused by

truncating the Fourier series. Applications to a variety of problems

will be discussed to demonstrate that the analytic approach remains a

valuable complement to purely numerical methods.

The talk is intended for students with an interest in actually

solving partial differential equations. It assumes a standard

background in undergraduate mathematics but not necessarily prior

exposure to the subject. The goal is to show that there is more to

separation of variables than is apparent from standard texts on

engineering mathematics.

It is by now well known that one cannot HEAR the shape of a

drum: There are many known examples of isospectral yet not isometric "drums". Recently we discovered that the sequences of integers formed by counting the nodal domains of successive eigenfunctions encode geometrical information, which can also be used to resolve spectral ambiguities. I shall discuss these sequences and indicate how the information stored in the nodal sequences can be deciphered.

We discuss a method for solving very large structured symmetric indefinite equation systems arising in optimization with interior point methods.

Many real-life economic models involve system dynamics, spatial distribution or uncertainty and lead to large-scale optimization problems. Such problems usually have a hidden structure: they are constructed by replication of some small generic block. The linear algebra subproblems which arise in optimization algorithms for such problems involve matrices which are not only sparse, but they additionally display a block-structure with many smaller blocks sparsely distributed in the large matrix.

We have developed a structure-exploiting parallel interior point solver for optimization problems. Its design uses object-orientated programming techniques. The progress OOPS (Object-Orientated Parallel Solver: http://www.maths.ed.ac.uk/~gondzio/parallel/solver.html) on a number of different computing platforms and achieves scalability on a number of different computing platforms. We illustrate its performance on a collection of problems with sizes reaching 10⁹ variables arising from asset liability management and portfolio optimization.

This is a joint work with Andreas Grothey.

Given a family of independent events in a probability space, the probability

that none of the events occurs is of course the product of the probabilities

that the individual events do not occur. If there is some dependence between the

events, however, then bounding the probability that none occurs is a much less

trivial matter. The Lov

/notices/events/abstracts/stochastic-analysis/mt05/m

In Clarendon Lab