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Andre-I Nikolaevich Tikhonov, ""

This book represents a fine contribution to the

current literature on the subject of ill posed problems.

Ill-posed problems include such classical problems of analysis

and algebra as differentiation of functions known only approxi-

mately, solution of integral equations of the first kind, summation

of Fourier series with approximate coefficients, analytical

continuation of functions, finding the inverse Laplace transform,

the Cauchy problem for the Laplace equation, solution of singular

or ill-conditioned systems of linear algebraic equations, and many

others, some of which are of great practical significance...

All such problems cabn be divided into two subclasses, namely, those of

recognition and those of design. The first subclass includes, among

others, problems of mathematical processing and interpretation of

data, as in nuclear-, plasma-, or radiophysics, electronics,

interpretation of geophysical observations, mineral (including

petroleum) prospecting, rocketry, nuclear reactor engineering, etc.

The second subclass includes many optimization problems, for

example, design of antenna or optical systems, optimal control,

and optimal economic planning.

This book deals with solutions of problems of this nature. It

defines the concept of an approximate solution of such problems

that is stable to small changes in the initial data and it examines in

detail methods of constructing solutions that are easily processed

on a computer.

The material will be

of interest to a wide variety of specialists in applied mathematics and

engineering and should be on the bookshelf of anyone interested in ill posed

problems. There are numerous examples and illustrations. The translator has

taken pains to insure that the English reads smoothly.

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