On the error estimation for a mixed type of interpolation

摘要

We analyse the error induced by the approximation of a function by an interpolation function which is a combination of algebraic and first-order trigonometric polynomials. We prove that, under certain conditions, this error can be expressed in a similar form as in the purely polynomial case. As an application we establish in closed form the local truncation error for a class of extended linear multistep methods of the Adams' type.