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Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling
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Nonlinear Least Squares for Inverse Problems - Theoretical Foundations and Step-by-Step Guide for Applications (Paperback, 2010 ed.)
Loot Price: R3,237
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Nonlinear Least Squares for Inverse Problems - Theoretical Foundations and Step-by-Step Guide for Applications (Paperback, 2010 ed.)
Series: Scientific Computation
Expected to ship within 10 - 15 working days
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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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