How strategy of approximation turned out to be successful?
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Approximation theory is a branch of mathematics, a quantitative part of functional analysis. Diophantine approximation deals with approximations of real numbers by rational numbers. Approximation usually occurs when an exact form or an exact numerical number is unknown or difficult to obtain
All versions of the HK model to be considered here study the opinion dynamics of communities of agents who are individually trying to determine the value of a certain parameter, where the agents know antecedently that the true value lies in the half-open interval 〈0, 1]. In the simplest version of the model, the agents simultaneously update their beliefs as to the value of the parameter by averaging over the beliefs of those other agents in the community whose beliefs are within a distance of ɛ from their own, for some given ɛ ∈ [0,1] (henceforth to be called “neighbors”; note that every agent counts as its own neighbor). To illustrate, Fig. 1 shows the evolution of the beliefs of twenty-five agents who, starting from different initial beliefs, repeatedly update in the said way, and where ɛ = .1. What we see are diverging converging groups.