Recent decades have seen a very rapid success in developing numerical methods
based on explicit control over approximation errors. It may be said that
nowadays a new direction is forming in numerical analysis, the main goal of
which is to develop methods ofreliable computations. In general, a reliable
numerical method must solve two basic problems: (a) generate a sequence of
approximations that converges to a solution and (b) verify the accuracy of these
approximations. A computer code for such a method must consist of two respective
blocks: solver and checker.
In this book, we are chiefly concerned with the problem (b) and try to present
the main