An Introduction to Inverse Problems with Applications

ISBN-13: 9783642441943 / Angielski / Miękka / 2014 / 246 str.

Francisco Duarte Moura Neto; Antonio Jose Da Silva Neto

Opis

Computational engineering/science uses a blend of applications, mathematical models and computations. Mathematical models require accurate approximations of their parameters, which are often viewed as solutions to inverse problems. Thus, the study of inverse problems is an integral part of computational engineering/science. This book presents several aspects of inverse problems along with needed prerequisite topics in numerical analysis and matrix algebra. If the reader has previously studied these prerequisites, then one can rapidly move to the inverse problems in chapters 4-8 on image restoration, thermal radiation, thermal characterization and heat transfer. "This text does provide a comprehensive introduction to inverse problems and fills a void in the literature". Robert E White, Professor of Mathematics, North Carolina State University

Recenzje

From the reviews:

"Book attempts to introduce the subject of inverse problems in a way that emphasizes practical methods for the solution of applied problems while also providing a general understanding of the subject. ... of interest to instructors who want to teach an introductory course in inverse problems with limited mathematics prerequisites to an audience of scientists and engineers at the advanced undergraduate or graduate level. ... book would also be accessible to graduate students in engineering and science for self study." (Brian Borchers, MAA Reviews, October, 2013)
"The authors of this textbook had a wide range of readers in mind. Their profiles encompass from honors undergraduate to graduate students and include mathematics or engineering researchers. ... it describes all different steps of a typical problem in Computational Sciences and Engineering ... . computer scientists as well as experts from the particular area of application are also among this book eventual readers." (Carlos A. De Moura, Zentralblatt MATH, Vol. 1264, 2013)

Spis treści

Road map.- Mathematical modeling.- Fundamental concepts in inverse problems.- Spectral analysis of an inverse problem.- Image restoration.- Radiative transfer and heat conduction.- Thermal characterization.- Heat conduction.- A general perspective.