Descript 
xiii, 351 pages : illustrations (some color) ; 26 cm 

text rdacontent 

unmediated rdamedia 

volume rdacarrier 
Series 
Computational science and engineering 

Computational science and engineering

Note 
Includes bibliographical references (pages 311347) and index 

Naíve reconstruction and inverse crimes  Illposedness in inverse problems  Truncated singular value decomposition  Tikhonov regularization  Total variation regularization  Besov space regularization using wavelets  Discretizationinvariance  Practical Xray tomography with limited data  Projects  Nonlinear inverse problems  Nonlinear inversion  Electrical impedance tomography  Simulation of noisy EIT data  Complex geometrical optics solutions  A regularized Dbar method for direct EIT  Other direct solution methods for EIT  Projects  Banach spaces and Hilbert spaces  Mappings and compact operators  Fourier transform and Sobolev spaces  Iterative solution of linear equations 

Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify illposed inverse problems arising in practice and how to design computational solution methods for them; explains computational approaches in a handson fashion, with related codes available on a website; and serves as a convenient entry point to practical inversion. The guiding linear inversion examples are the problem of image blurring, xray tomography, and backward parabolic problems, including heat transfer; electrical impedance tomography is used as the guiding nonlinear inversion example. The book's nonlinear material combines the analyticgeometric research tradition and the regularizationbased school of thought in a fruitful manner, paving the way to new theorems and algorithms for nonlinear inverse problems. Furthermore, it is the only mathematical textbook with a thorough treatment of electrical impedance tomography, and these sections are suitable for beginning and experienced researchers in mathematics and engineering. Linear and Nonlinear Inverse Problems with Practical Applications is wellsuited for students in mathematics, engineering, physics, or computer science who wish to learn computational inversion (inverse problems). Professors will find that the exercises and project work topics make this a suitable textbook for advanced undergraduate and graduate courses on inverse problems. Researchers developing largescale inversion methods for linear or nonlinear inverse problems, as well as engineers working in research and development departments at hightech companies and in electrical impedance tomography, will also find this a valuable guide 
Subject 
Inverse problems (Differential equations)


Inverse problems (Differential equations) fast (OCoLC)fst00978098

Alt Author 
Siltanen, Samuli, author

