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There is proposed a method for improving the convergence of Fourier series byfunction systems, orthogonal at the segment, the application of which allowsfor smooth functions to receive uniformly convergent series. There is alsoproposed the method of phantom nodes improving the convergence of interpolationpolynomials on systems of orthogonal functions, the application of which inmany cases can significantly reduce the interpolation errors of thesepolynomials. The results of calculations are given at test cases using theproposed methods for trigonometric Fourier series; these calculationsillustrate the high efficiency of these methods. Undoubtedly, the proposedmethod of phantom knots requires further theoretical studies.

Method of improvement of convergence Fourier series and interpoliation polynomials in orthogonal functions