The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.

Ten years ago, the term "defect correction" was introduced to characterize a class of methods for the improvement of an approximate solution of an operator equation. This class includes many well-known techniques (e.g. Newton's method) but also some novel approaches which have turned out to be quite efficient. Meanwhile a large number of papers and reports, scattered over many journals and institutions, have appeared in this area. Therefore, a working conference on "Error Asymptotics and Defect Corrections" was organized by K. Bohmer, V. Pereyra and H. J. Stetter at the Mathematisches Forschungsinstitut Oberwolfach in July 1983, a meeting which aimed at bringing together a good number of the scientists who are active in this field. Altogether 26 persons attended, whose interests covered a wide spectrum from theoretical analyses to applications where defect corrections may be utilized; a list of the participants may be found in the Appendix. Most of the colleagues who presented formal lectures at the meeting agreed to publish their reports in this volume. It would be presumptuous to call this book a state-of-the-art report in defect corrections. It is rather a collection of snapshots of activities which have been going on in a number of segments on the frontiers of this area. No systematic coverage has been attempted. Some articles focus strongly on the basic concepts of defect correction; but in the majority of the contributions the defect correction ideas appear rather as instruments for the attainment of some specified goal.