Abstract:
For arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on some uniform grid. No additional assumptions about the functions are required. The construction of such a formula is connected with the properties of local Bernstein polynomials and the Riemann zeta function. Numerical results for the interpolation of functions of the Riemann, Weierstrass, Besicovitch, and Takagi types are presented.
Keywords:interpolation, local Bernstein polynomials, binomial coefficients, Euler gamma functions, multiplicative Gauss formula, Riemann zeta function, Riemann type functions, Weierstrass type functions, Besicovich type functions, Takagi type functions.
UDC:519.652+517.589
Presented:S. N. Vassilyev Received: 13.09.2023 Revised: 10.04.2024 Accepted: 26.04.2024
