Mollification Method and the Numerical Solution of Ill-Posed Problems

Over the past twenty years, the subject of applied inverse theory (ill-posed problems) has expanded from a collection of individual techniques to a rich, highly developed branch of applied mathematics. The Mollification Method and the Numerical Solution of Ill-Posed Problems offers a self-contained introduction to several of the most important practical computational methods that have been successfully applied to a wide range of ill-posed problems. The book examines the mollification method and its multiple applications when used as a space marching method. These computations are compared with various other methods used to arrive at the same numerical results. Of special interest is a novel treatment of the two-dimensional inverse heat conduction problem on a bounded domain. There is a strong emphasis on computation, supplemented by numerous exercises, examples, and illustrations. Unlike most books on ill-posed problems, this volume contains all the motivations, proofs, algorithms, and exercises necessary to fully understand the subject. Materials are presented in clear simple language to make the subject accessible to readers with little or no background in ill-posed problems. For nonmathematicians, an overview of essential mathematical tools is contained in an appendix. References at the end of each chapter are supplemented with comments by the author, and a second appendix offers up-to-date citings of literature on the inverse heat conduction problem to aid readers in further research. An excellent text for upper-level undergraduate or first-year graduate courses on computational methods for inverse ill-posed problems, this book will also serve as a valuable reference work for professionals interested in modeling inverse phenomena.Murio, Diego A. is the author of 'Mollification Method and the Numerical Solution of Ill-Posed Problems' with ISBN 9780471594086 and ISBN 0471594083.