Guy Chavent

(Author)

Nonlinear Least Squares for Inverse Problems: Theoretical Foundations and Step-By-Step Guide for Applications (2010)Paperback - 2010, 14 March 2012

Nonlinear Least Squares for Inverse Problems: Theoretical Foundations and Step-By-Step Guide for Applications (2010)
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Part of Series
Scientific Computation
Print Length
360 pages
Language
English
Publisher
Springer
Date Published
14 Mar 2012
ISBN-10
9400730608
ISBN-13
9789400730601

Description

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..

Product Details

Author:
Guy Chavent
Book Edition:
2010
Book Format:
Paperback
Country of Origin:
NL
Date Published:
14 March 2012
Dimensions:
23.39 x 15.6 x 1.98 cm
ISBN-10:
9400730608
ISBN-13:
9789400730601
Language:
English
Location:
Dordrecht
Pages:
360
Publisher:
Weight:
526.17 gm

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