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Iterative Methods for Approximate Solution of Inverse Problems

A.B. Bakushinsky and M. Yu. Kokurin
Publisher: 
Springer Verlag
Publication Date: 
2004
Number of Pages: 
287
Format: 
Hardcover
Series: 
Mathematics and Its Applications
Price: 
99.00
ISBN: 
1-4020-3121-1
Category: 
Monograph
[Reviewed by
Jeffrey A. Graham
, on
01/26/2006
]

Iterative Methods for Approximate Solutions of Inverse Problems contains primarily a rigorous development of a method for constructing iterative methods.  The best audience for this book is a well-trained functional analyst with an interest in inverse problems.  Most of the book is highly technical — at one point I counted five consecutive pages devoted to computations and equations in support of a proof.  This style of presentation is enough to make all but the most ardent functional analysts weary.

There are some applications presented in the later chapters.  However, they are presented without computer code or much in the way of implementation detail.  The graphics that summarize the results are a bit crude and their placement in the text is awkward.  A person trying to match a graph to an example spends many frustrating minutes flipping from page to page trying to match things up.

The writing style is very technical and there is some idiosyncratic language used.  Either the book is a slightly awkward translation into English or the authors' fluency in English is lacking a little.  Better editing could have solved that problem and it is really more of an annoyance than a hindrance to understanding.

In summary, the book contains some pretty good mathematics, but the presentation of the material leaves quite a bit to be desired.  Extracting useful information out of this book will require much effort. 


Jeffrey A. Graham teaches at Susquehanna University. His interests include numerical analysis, differential equations, inverse problems, and mathematical biology.
Dedication. Acknowledgments. Introduction.- 1. Irregular Equations as Ill-Posed Problems.- 2. Regularization Methods for Linear Equations.- 3. Parametric Approximations of Solutions to Nonlinear Operator Equations.- 4. Iterative Processes on the Basis of Parametric Approximations.- 5. Stable Iterative Processes.- 6. Applications of Iterative Methods.- 7. Notes.- References.- Index.

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