Measuring-polynomial processing of input data of a computer system

Purpose of research. The purpose of this study is to construct approximation grid nodes in the measurement-polynomial processing of input data of a computer system in the coefficient inverse problem for an algebraic polynomial, including for the equation of beam deflections when solving the inverse Cauchy problem. Methods. The main scientific methods used in this study are methods of regularization, measurement reduction, linear Lagrangian approximation, and numerical methods. Since when deriving explicit formulas in the radicals of the roots of the resolving equations for the optimal design of the approximation grid nodes according to Abel’s theorem, a limitation is imposed on the degree of the equations, in this article, in solving the problem for an algebraic polynomial with a prescribed coefficient of the second lowest term, it is proposed to use the Chebyshev alternance of extremal polynomials. Results. The result of the study is a technique for optimizing the approximation grid, minimizing the influence of the input data error with a uniform continuous norm of absolute errors on the accuracy of solving the problem by minimizing the Lebesgue function. The proposal to apply a modification of Chebyshev polynomials to the optimal approximation grid is substantiated. Conclusion. This article proposes a formalization of the problem of minimizing the influence of the input data error on the accuracy of calculating the coefficients of an algebraic polynomial in a measurement and computing system by selecting the nodes of the approximation grid through the Chebyshev alternance.