Frontiers of Numerical Analysis Durham 2004

TheEleventh LMS-EPSRCComputational MathematicsandScienti'cC- puting Summer School was held at the University of Durham, UK, from the 4th of July to the 9th of July 2004. This was the third of these schools to be held in Durham, having previously been hosted by the University of L- caster and the University of Leicester. The purpose of the summer school was to present high quality instructional courses on topics at the forefront of computational mathematics and scienti'c computing research to postgra- ate students. The main speakers were Emmanuel Candes, Markus Melenk, Joe Monaghan and Alex Schweitzer. This volume presents written contributions three of our speakers which are more comprehensive versions of the high quality lecture notes which were distributedtoparticipantsduringthemeeting.Wearealsoextremelypleased that Angela Kunoth was able to make an additional contribution from the ill-fated ?rst week. At the time of writing it is now more than two years since we ?rst contacted theguestspeakersandduringthatperiodtheyhavegivensigni'cantportions of their time to making the summer school, and this volume, a success. We wouldliketothankallofthemforthecarewhichtheytookinthepreparation and delivery of their material.