Nonlinear Least Squares for Inverse Problems - Theoretical Foundations and Step-by-Step Guide for Applications (Hardcover, 2010 ed.)

The domain of inverse problems has experienced a rapid expansion, driven by the increase in computing power and the progress in numerical modeling. When I started working on this domain years ago, I became somehow fr- tratedtoseethatmyfriendsworkingonmodelingwhereproducingexistence, uniqueness, and stability results for the solution of their equations, but that I was most of the time limited, because of the nonlinearity of the problem, to provethatmyleastsquaresobjectivefunctionwasdi?erentiable....Butwith my experience growing, I became convinced that, after the inverse problem has been properly trimmed, the ?nal least squares problem, the one solved on the computer, should be Quadratically (Q)-wellposed, thatis, both we- posed and optimizable: optimizability ensures that a global minimizer of the least squares function can actually be found using e?cient local optimization algorithms, and wellposedness that this minimizer is stable with respect to perturbation of the data. But the vast majority of inverse problems are nonlinear, and the clas- cal mathematical tools available for their analysis fail to bring answers to these crucial questions: for example, compactness will ensure existence, but provides no uniqueness results, and brings no information on the presence or absenceofparasiticlocalminimaorstationarypoints..

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Scientific Computation
Release date:	October 2009
First published:	2010
Authors:	Guy Chavent
Dimensions:	235 x 155 x 28mm (L x W x T)
Format:	Hardcover
Pages:	360
Edition:	2010 ed.
ISBN-13:	978-90-481-2784-9
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science
LSN:	90-481-2784-X
Barcode:	9789048127849

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