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Minimax algorithms in problems of numerical analysis. (Minimaksnye algoritmy v zadachakh chislennogo analiza.) (Russian. English summary) Zbl 0717.65037
Complexity and optimality of algorithms in numerical analysis are studied. Problems and algorithms are treated with a general framework based on the minimax concept of optimality. Adaptive algorithms and their implementation as well as game-theoretic methods for constructing optimal algorithms are considered. The central role of sequentially-optimal algorithms results from the fact that the notion of sequential optimality suits a number of real computational processes better than the traditional notions. The following chapters are contained: 1. General model of computation; 2. Numerical integration; 3. Recovery of functions using their values; 4. Search for a global extremum; 5. Some special classes of extremal problems.
Reviewer: H.Benker

65K05 Numerical mathematical programming methods
65D32 Numerical quadrature and cubature formulas
65Y20 Complexity and performance of numerical algorithms
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
68Q25 Analysis of algorithms and problem complexity