|
The method of interpolation in classical numerical analysis is a basic and fundamental
one. The polynomial approximation for the points in 2-dimensional Euclidean space
is well-known to us and various methods, viz., Newton’s divided difference
interpolation method, Lagrange’s interpolation method, etc. (Berrut and Trefethen,
2004; and Veerarajan and Ramachandra, 2005), are already established to furnish
this part of numerical analysis. Nevertheless, the interpolation methods
(Scarborough, 1966) so far developed for the points of three or higher dimensional
Euclidean spaces are not that much handy as most of these methods require detail
knowledge of mathematical analysis or they are bounded by some restrictions.
In this paper, we propose a compact interpolation method to interpolate points
in 3D. Similar methods can be established for n-dimensional interpolations
(n > 3). A new interpolation operator is defined and used here. For 2-dimensional
interpolation, this operator coincides with the divided difference operator. Some
theorems in support of this are also established.
The paper is organized as follows: In Section 2 the interpolation operator is
defined and discussed. In Section 3 the interpolation method is discussed and the
corresponding algorithm is presented. Subsequently, in Section 4 a numerical
example is presented in support of the formula obtained, and finally, the conclusion
is offered.
|
