Minimax Models in the Theory of Numerical Models

Methods for estimating the efficiency of computational algorithms and problems of their optimality are studied within the framework of a general computation model in this text. Close attention is paid to adaptive (sequential) computational algorithms.

The efficiency of computational methods and the choice of the most efficient methods for solving a specific problem or a specific class of problems have always played an important role in numerical analysis. Optimization of the computerized solution process is now a major problem of applied mathematics, which stimulates the search for new computational methods and ways to implement them. In "Minimax Models in the theory of Numerical Methods", methods for estimating the efficiency of computational algorithms and problems of their optimality are studied within the framework of a general computation model. The subjects dealt with in this are very different from the traditional subjects of computational methods. Close attention is paid to adaptive (sequential) computational algorithms, the process of computation being regarded as a controlled process and the algorithm as a control strategy. This approach allows methods of game theory and other methods of operations research and systems analysis to be widely used for constructing optimal algorithms. The goal underlying the study of the various comutation models dealt with in this title is the construction of concrete numerical algorithms admitting programme implementation. The central role belongs to the concept of a sequentially optimal algorithms, which in many cases reflects the characterics of real-life computational processes more fully than the traditional optimality concepts.