000 03759nam a22005055i 4500
001 978-90-481-2785-6
003 DE-He213
005 20140220084556.0
007 cr nn 008mamaa
008 100715s2010 ne | s |||| 0|eng d
020 _a9789048127856
_9978-90-481-2785-6
024 7 _a10.1007/978-90-481-2785-6
_2doi
050 4 _aTA342-343
072 7 _aPBWH
_2bicssc
072 7 _aTBJ
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aTEC009060
_2bisacsh
082 0 4 _a003.3
_223
100 1 _aChavent, Guy.
_eauthor.
245 1 0 _aNonlinear Least Squares for Inverse Problems
_h[electronic resource] :
_bTheoretical Foundations and Step-by-Step Guide for Applications /
_cby Guy Chavent.
264 1 _aDordrecht :
_bSpringer Netherlands,
_c2010.
300 _aXIV, 360p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aScientific Computation,
_x1434-8322
505 0 _aNonlinear Least Squares -- Nonlinear Inverse Problems: Examples and Difficulties -- Computing Derivatives -- Choosing a Parameterization -- Output Least Squares Identifiability and Quadratically Wellposed NLS Problems -- Regularization of Nonlinear Least Squares Problems -- A generalization of convex sets -- Quasi-Convex Sets -- Strictly Quasi-Convex Sets -- Deflection Conditions for the Strict Quasi-convexity of Sets.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aMathematical physics.
650 0 _aEngineering mathematics.
650 1 4 _aMathematics.
650 2 4 _aMathematical Modeling and Industrial Mathematics.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aCalculus of Variations and Optimal Control, Optimization.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789048127849
830 0 _aScientific Computation,
_x1434-8322
856 4 0 _uhttp://dx.doi.org/10.1007/978-90-481-2785-6
912 _aZDB-2-PHA
999 _c113219
_d113219