# Derivation of a general mixed interpolation formula

Chakrabarti, A and Hamsapriye, * (1996) Derivation of a general mixed interpolation formula. In: Journal of Computational and Applied Mathematics, 70 (1). pp. 161-172.

 PDF Derivation_of_a_general_mixed_interpolation_formula.pdf Restricted to Registered users only Download (499Kb) | Request a copy

## Abstract

A general procedure is developed to derive a mixed interpolation formula for approximating any (n + 1) times differentiable function f(x), for x \in [0,nh], by a function $f_n(x)$ of the type $f_n(x)=aU_1(kx) + bU_2(kx)+\sum^{n-2}_{i=0}cix^i$, interpolating points being the ones given by $x_j = jh,(h > 0),j = O,1, . . . . . n,$ where $U_1(kx)$ and $U_2 (kx)$ are the two linearly independent solutions of a suitable second order Ordinary Differential Equation (ODE) and k > 0 is an appropriately chosen parameter. The results for the particular case when $U_1(kx)$ and $U_2(kx)$ represent the trigonometric functions follow easily. An analysis of the error is also discussed and specific numerical examples are included for the sake of comparison with the known interpolation formulae. Tables showing the comparison of the maximum errors occuring in the use of the various interpolation formulae has also been presented for some specially chosen functions.

Item Type: Journal Article Copyright of this article belongs to Elsevier. Mixed interpolation;Oscillation theory;Polynomial interpolation;Green's function Division of Physical & Mathematical Sciences > Mathematics 22 Dec 2006 19 Sep 2010 04:33 http://eprints.iisc.ernet.in/id/eprint/9171