Comparative study of the least squares approximation of the modified Bessel function

摘要

The least squares problem of the modified Bessel function of the second kind has been considered in this study with the Fourier series, Tchebycheff and Legendre approximation. Numerical evidence shows that the Gibbs phenomenon exists in the approximation with the truncated Fourier series, thus, giving poor convergence results compared with the other polynomial bases. For the latter two cases, the Legendre series perform better than Tchebycheff series in terms of the L~2 norm of the relative errors for each order of the polynomial approximation, and the ratio of the L~2 norm of the relative errors from the corresponding approximation seems to be a constant value of 1.3.