Special issue: Applied Computational Inverse Problems

Many questions in science and engineering are concerned with the determination of causes for observed effects. These questions give rise to mathematical problems known as inverse problems. The investigation of inverse problems and their numerical solution is currently receiving considerable attention with many conferences and workshops. It is the purpose of this issue to present new results on the analysis of inverse problems in several application areas, and to discuss numerical methods for their solution. The 16 contributions in this issue illustrate the vigor and breadth of current research. This issue grew out of the workshop “Applied Computational Inverse Problems” held at CNR in Florence, 22–25, March, 2004. The workshop was organized by Elisa Francini, Fiorella Sgallari, and Giorgio Talenti, and was part of the research project “Theoretical and Computational Aspects of Inverse Problems” funded by GNCS-GNAMPA(INDAM). This project involved 40 researchers at universities in Bari, Bologna, Florence, Genova, Milan, Naples, Rome, Trieste, and Udine. Research on inverse problems is carried out by scientists with diverse expertise and interests. It was the purpose of the workshop to bring together mathematicians who work on the analysis of inverse problems with researchers interested in the development and analysis of numerical methods for their solution. Results from analysis of inverse problems are helpful for the understanding of the performance of numerical methods, as well as for the development of new computational techniques and software. Conversely, the behavior of computational methods and their success in providing meaningful solutions is likely to spur new analysis of inverse problems. Many of the contributions to this issue are authored or co-authored by Italian scientists illustrating the considerable research on inverse problems that is taking place in Italy today. Sincerely, Lothar Reichel, Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA. E-mail address: reichel@math.kent.edu Fiorella Sgallari, Department of Mathematics CIRAM, University of Bologna, Via Saragozza 8, 40123 Bologna, Italy.