EAN: 9783030633455

AN INTRODUCTION TO THE MATHEMATICAL THEORY OF I...

This graduate-level textbook introduces the reader to the area of inverse problems  vital to
many fields including geophysical exploration  system identification  nondestructive testing 
and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered
with ill-posed problems  analyzing basic properties of regularization methods for ill-posed
problems via several simple analytical and numerical examples. The book also 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. Ultimately  the text discusses theoretical results as well as numerical procedures
for the inverse problems  including many exercises and illustrations to complement coursework
in mathematics and engineering. This updated text includes a new chapter on the theory of
nonlinear inverse problems in response to the field's growing popularity  as well as a new
section on the interior transmission eigenvalue problem which complements the Sturm-Liouville
problem and which has received great attention since the previous edition was published.

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