Diophantine Approximations of Algebraic Irrationalities and Stability Theorems for Polynomial Decision Rules

摘要

The theoretical aspects of the decision rules stability problem are considered in the article. The new metric theorems of the stability of the polynomial decision rules are proven. These theorems are sequent from the well-known results of approximating irrationalities by rational numbers obtained by Liouville, Roth and Khinchin. The problem of optimal correlation between deterministic and stochastic methods and quality criterion in pattern recognition problems is also discussed.