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A variant of self-similar approximation theory is suggested, permitting aneasy and accurate summation of divergent series consisting of only a few terms.The method is based on a power-law algebraic transformation, whose powers playthe role of control functions governing the fastest convergence of therenormalized series. A striking relation between the theory of criticalphenomena and optimal control theory is discovered: The critical indices arefound to be directly related to limits of control functions at critical points.The method is applied to calculating the critical indices for several difficultproblems. The results are in very good agreement with accurate numerical data.Comment: 1 file, 5 pages, RevTe

Critical Indices as Limits of Control Functions