Nonlinear Least Squares for Inverse Problems: Theoretical Foundations and Step-by-Step Guide for Applications (Scientific Computation) - Softcover

Chavent, Guy

Softcover

ISBN 10: 9400730608 ISBN 13: 9789400730601

Verlag: Springer, 2012

Inhaltsangabe

This book provides a step-by-step introduction to the least squares resolution of nonlinear inverse problems. For readers interested in projection of non-convex sets, it also presents the geometric theory of quasi-convex and strictly quasi-convex sets.

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Über die Autorin bzw. den Autor

Background: Ecole Polytechnique (Paris, 1965),

Ecole Nationale Supérieure des Télécommunications (Paris,1968),

Paris-6 University (Ph. D., 1971).

Professor Chavent joined the Faculty of Paris 9-Dauphine in 1971. He is now an emeritus professor from this university. During the same span of time, he ran a research project at INRIA (Institut National de Recherche en Informatique et en Automatique), focused on industrial inverse problems (oil production and exploration, nuclear reactors, ground water management…).

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This book provides an introduction into the least squares resolution of nonlinear inverse problems. The first goal is to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, i.e. both wellposedness and optimizability. Using the results, the applicability of various regularization techniques can be checked. The second objective of the book is to present frequent practical issues when solving NLS problems. Application oriented readers will find a detailed analysis of problems on the reduction to finite dimensions, the algebraic determination of derivatives (sensitivity functions versus adjoint method), the determination of the number of retrievable parameters, the choice of parametrization (multiscale, adaptive) and the optimization step, and the general organization of the inversion code. Special attention is paid to parasitic local minima, which can stop the optimizer far from the global minimum: multiscale parametrization is shown to be an efficient remedy in many cases, and a new condition is given to check both wellposedness and the absence of parasitic local minima.

For readers that are interested in projection on non-convex sets, Part II of this book presents the geometric theory of quasi-convex and strictly quasi-convex (s.q.c.) sets. S.q.c. sets can be recognized by their finite curvature and limited deflection and possess a neighborhood where the projection is well-behaved.

Throughout the book, each chapter starts with an overview of the presented concepts and results.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 9400730608
• ISBN 13: 9789400730601
• Einband: Taschenbuch
• Anzahl der Seiten: 376
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland