Nonlinear Least Squares for Inverse Problems

Released on by Guy Chavent
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  • Nonlinear Least Squares for Inverse Problems Book Detail

  • Author : Guy Chavent
  • Release Date : 2010-03-14
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 366
  • ISBN 13 : 9048127858
  • File Size : 94,94 MB
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Nonlinear Least Squares for Inverse Problems by Guy Chavent PDF Summary

Book 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....

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Inverse Problems in Wave Propagation

Inverse Problems in Wave Propagation

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Inverse problems in wave propagation occur in geophysics, ocean acoustics, civil and environmental engineering, ultrasonic non-destructive testing, biomedical u