Optimizarea metodelor numerice, aplicate la interpolarea funcţiilor [Articol]

Abstract

The paper deals with interpolating functions based on uniform and non-uniform structures. Functions are either discreet or rather complicated. In the literature, the calculation formulas of the interpolation polynomial Newton, Gauss, Stirling, Bessel and Heverette in the equidistant nodes are specified. But these formulas are based on the application of a recurrent formula for calculating the value of the polynomial for any point investigated. Thus, many of the calculations are repeated. In order to optimize the work, the paper investigated the possibility of determining the coefficients of the Newton interpolation polynomials in normal form without performing repetitions. The paper examines the following aspects:• description of numerical methods of interpolation of functions; • the theoretical determination of the coefficients of the formulas in the definition of the interpolation polynomials for a uniform discrete network for the concrete number of nodes; • defining the interpolation polymorph formulas by one or two parameters based on the determined coefficients; • a programming the formulas defined in the interpolation of functions in discrete or continuous mode. For each variant used, examples of application are presented.