000 03523nam a22004935i 4500
001 978-1-4419-8474-6
003 DE-He213
005 20140220083728.0
007 cr nn 008mamaa
008 110323s2011 xxu| s |||| 0|eng d
020 _a9781441984746
_9978-1-4419-8474-6
024 7 _a10.1007/978-1-4419-8474-6
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aKirsch, Andreas.
_eauthor.
245 1 3 _aAn Introduction to the Mathematical Theory of Inverse Problems
_h[electronic resource] /
_cby Andreas Kirsch.
250 _a2.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2011.
300 _aXIV, 310 p.
_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 ;
_v120
505 0 _a Introduction and Basic Concepts -- Regularization Theory for Equations of the First Kind -- Regularization by Discretization -- Inverse Eigenvalue Problems --  An Inverse Problem in Electrical Impedance Tomography -- An Inverse Scattering Problem -- References -- Index.
520 _aThis book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography.   The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples.   The second part of the book presents three special nonlinear inverse problems in detail - the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed.   In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph.   The book is highly illustrated and contains many exercises. This together with the choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students in mathematics and engineering.
650 0 _aMathematics.
650 0 _aDifferential Equations.
650 0 _aDifferential equations, partial.
650 0 _aEngineering mathematics.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aOrdinary Differential Equations.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441984739
830 0 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v120
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-8474-6
912 _aZDB-2-SMA
999 _c106002
_d106002