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One of the most important chapters in modern functional analysis is
the theory of approximate methods for solution of various
mathematical problems. Besides providing considerably simplified
approaches to numerical methods, the ideas of functional analysis
have also given rise to essentially new computation schemes in
problems of linear algebra, differential and integral equations,
nonlinear analysis, and so on. The general theory of approximate
methods includes many known fundamental results. We refer to the
classical work of Kantorovich; the investigations of projection
methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered
by Mikhlin and Pol'skii; Tikho nov's methods for approximate
solution of ill-posed problems; the general theory of difference
schemes; and so on. During the past decade, the Voronezh seminar on
functional analysis has systematically discussed various questions
related to numerical methods; several advanced courses have been
held at Voronezh Uni versity on the application of functional
analysis to numerical mathe matics. Some of this research is
summarized in the present monograph. The authors' aim has not been
to give an exhaustive account, even of the principal known results.
The book consists of five chapters."
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