000 04298nam a22005055i 4500
001 978-1-4614-8827-9
003 DE-He213
005 20140220082503.0
007 cr nn 008mamaa
008 131028s2014 xxu| s |||| 0|eng d
020 _a9781461488279
_9978-1-4614-8827-9
024 7 _a10.1007/978-1-4614-8827-9
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aCakoni, Fioralba.
_eauthor.
245 1 2 _aA Qualitative Approach to Inverse Scattering Theory
_h[electronic resource] /
_cby Fioralba Cakoni, David Colton.
264 1 _aBoston, MA :
_bSpringer US :
_bImprint: Springer,
_c2014.
300 _aX, 297 p. 15 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v188
505 0 _a1. Functional Analysis and Sobolev Spaces -- 2. Ill-Posed Problems -- 3. Scattering by Imperfect Conductors -- 4. Inverse Scattering Problems for Imperfect Conductors -- 5. Scattering by Orthotropic Media -- 6. Inverse Scattering Problems for Orthotropic Media -- 7. Factorization Methods -- 8. Mixed Boundary Value Problems -- 9. Inverse Spectral Problems for Transmission Eigenvalues -- 10. A Glimpse at Maxwell's Equations.
520 _aInverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to the inverse scattering problem which avoids the incorrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques. These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties without making any weak scattering assumption and using essentially no a priori information on the nature of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on the use of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posed problems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an earlier book by the authors published by Springer titled Qualitative Methods in Inverse Scattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized and easy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to the field as well as those who could benefit from such a nice codified collection of profitable results combined in one bound volume. SIAM Review, 2006
650 0 _aMathematics.
650 0 _aFourier analysis.
650 0 _aDifferential equations, partial.
650 0 _aComputer engineering.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aElectrical Engineering.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
650 2 4 _aFourier Analysis.
700 1 _aColton, David.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461488262
830 0 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v188
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-8827-9
912 _aZDB-2-SMA
999 _c92256
_d92256