Information Processing Model in the Coefficient Inverse Problem for an Algebraic Polynomial

The purpose of research is to develop a model for describing and evaluating the effectiveness of solving the coefficient inverse problem of analyzing and processing information about an algebraic polynomial with given coefficients of terms of lower degrees under the influence of input data error on the solution efficiency.

Methods. As a basic mathematical apparatus, the methodology for solving inverse problems with the approximation of functions by the Lagrange interpolation polynomial is used. Under the conditions of a uniform continuous error rate of the input data, when evaluating the efficiency of solving the coefficient inverse problem, it is proposed to use the minimum value of the objective function in the form of the minimum of the Lebesgue function. When deriving explicit formulas for the optimal plan of coordinates of the nodes of the approximation grid, it is proposed to apply the alternance characteristic of the extremal polynomial.

Results. As the basic elements of a mathematical model for analyzing and processing information about an algebraic polynomial in solving a coefficient inverse problem, Lagrange interpolation polynomials were used with a numerical estimate of the solution efficiency by the value of the minimum of the Lebesgue function.

Conclusion. In the course of the research, we solved the problem of developing a model for describing and evaluating the efficiency of the coefficient inverse problem of analyzing and processing information about an algebraic polynomial with given coefficients of terms of lower degrees and with the influence of the input data error on the accuracy of the solution. It is shown that to quantify the effectiveness of solving the problem, one should use the value of the objective function in the form of the minimum of the Lebesgue function, and to calculate the coefficients of the approximate polynomial, use the Lagrange interpolation polynomial.

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