Abstract
Questions on interpolation of functions with Lagrange polynomials are discussed. The Runge phenomenon is considered, when a sequence of Lagrange polynomials does not converge to an interpolated function uniformly. It is shown that the choice of roots of the Chebyshev polynomials as interpolation nodes provides more precise approximation than the interpolation by equidistant nodes. The Chebyshev polynomials are remarkable in sense that they admit least deviation from zero among all monic polynomials of the same degree. Сalculations and drawing graphs were performed using Maple program.
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