Daniel Kressner

Semi-automatic Generation of Web-Based Computing Environments for Software Libraries

e-Science encompasses computational science and adds the new dimension of the routine sharing of distributed computational, data, instruments and specialist resources. This paper describes the £120M UK ‘e-Science’ initiative, focusing on the ‘Core Programme’. The majority of the funding is for large-scale e-Science pilot projects in many areas of science and engineering. The pilot e-Science projects that have been announced to date are briefly described. These projects span a range of disciplines from particle physics and astronomy to engineering and healthcare, and illustrate the breadth of the UK e-Science Programme. The requirements of these projects and the recent directions in developments of open source middleware have provided direction for the roadmap of development within the Core Programme. The middleware infrastructure needed to support e-Science projects must permit routine the sharing of any remote resources as well as supporting effective collaboration between groups of scientists. Such an infrastructure is commonly referred to as the Grid. The focus of the paper is on the Core Programme that has been created in order to advance the development of robust and generic Grid middleware in collaboration with industry. The key elements of the Core Programme will be outlined including details of a UK e-Science Grid.

Krylov Subspace Methods for Linear Systems with Tensor Product Structure

The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on a

Block variants of Hammarling's method for solving Lyapunov equations

d

Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems

-dimensional hypercube. Linear systems with tensor product structure can be regarded as linear matrix equations for

Implicit QR algorithms for palindromic and even eigenvalue problems

d=2

A block Newton method for nonlinear eigenvalue problems

and appear to be their most natural extension for

Structured Eigenvalue Condition Numbers

d>2

Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems

. A standard Krylov subspace method applied to such a linear system suffers from the curse of dimensionality and has a computational cost that grows exponentially with

Skew-Hamiltonian and Hamiltonian Eigenvalue Problems: Theory, Algorithms and Applications

d

A fast algorithm for subspace state-space system identification via exploitation of the displacement structure

. The key to breaking the curse is to note that the solution can often be very well approximated by a vector of low tensor rank. We propose and analyze a new class of methods, so-called tensor Krylov subspace methods, which exploit this fact and attain a computational cost that grows linearly with