minimax

On an Inner Estimate of a Convex Body by the Lebesgue Set of Convex Differentiable Function

Authors: Dudov S. I., Abramova V. V.

A finite-dimentional problem of embedding the largest by the inclusion of lower Lebesgue set of given convex function f(x) in a given convex body D ⊂ R p is considered. This problem is the generalization of the problem of inscribed ball (function f(x) is some norm, and the Lebesgue sets are the corresponding balls). The function f(x) must be differentiable on R p possibly expending the point 0 p and 0 p is the uniqueness point of minimum. Mathematical formalization of this problem is proposed in the form of finding maximin of a function of the difference of arguments.

About the Retrofit of the Valle’e-Poussin’s Algorithm for Approximations of Multivalued Mappings by Algebraic Polynomial with Type Constraint Equality

Authors: Vygodchikova I. Y.

The discrete approximation of noisy data by algebraic polynomial with restriction of type equality is studied. The aimof the investigation is to obtain the fundamental properties of solution of the problem and development by them the new algorithm, more effective, in comparison with existing methods of the solution. The tasks of the research — gets the properties of the solution of the problem, presentation of the algorithm and the demonstration of its implementation. Research methodology continues P. L. Chebyshjov’s and Valle-Pussen’s method. Results.