An error bound for Lagrange interpolation of low-pass functions (Corresp.)

The well-known error formula for Lagrange interpolation is used to derive an expression for a truncation error bound in terms of the sampling rate and Nyquist frequency for regular samples and central interpolation. The proof is restricted to pulse-type functions possessing a Fourier transform. The formula finds application to the estimation of convergence rate in iterative interpolation, thus providing a criterion for the choice of sampling rate to achieve a specified truncation error level in a given number of steps. The formula can also be used as a guide when the samples are not regular but fairly evenly distributed.