Abstract
Lagrange polynomials are widely used as interpolation functions in engineering. But polynomials of high degree exhibit occasionally considerable oscillation, hence calculated values by polynomials are often inaccurate. Indeed, C. Runge proved that equidistant interpolation over |x|≤5 to the function f(x)=1/(1+x2) diverges for |x|>3.63…. In order to improve an accuracy of the approximation, new interpolation functions using finite Fourier series are proposed. Several numerical experiments are performed to check the validity of the proposed method. It is found that the present interpolation functions are more reliable and efficient than Lagrange polynomials.
