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, fexample, 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.