Acta Numerica surveys annually the most important developments in numerical mathematics and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important and timely developments in a manner accessible to the wider community of professionals with an interest in scientific computing. Acta Numerica volumes have proved to be a valuable tool not only for researchers and professionals wishing to develop their understanding of numerical techniques and algorithms and follow new developments, but also as an advanced teaching aid at colleges and universities. Many of the original articles have been used as the prime resource for graduate courses. This particular volume was originally published in 2003.