Abstract:
Interpolation is a technique that calculates the unknown values from known given values within
a certain range. Whereas the process of calculating unknown values beyond a certain given
range is called extrapolation. However, the term interpolation includes extrapolation. Many
operators require weak interpolation theory to accurately describe their cartographic properties. For
example, Anthony P.Austin (2016) discussed several topics related to interpolation and how it is
used in numerical analysis. Biswajit Das, Dhritikesh Chakrabarty (2016) had developed an
interpolation formula derived from Lagrange’s interpolation formula. The formula obtained had
been applied to represent the numerical data, on the total population of India by a suitable
polynomial. Slawomir Sujecki (2013) proposed an extension of the concept of the Taylor series to
arbitrary functions that are physically meaningful. The prime objective of our work is to construct a
model for interpolation to get a better approximation compared to some existing methods. In this
research, we aimed to approximate the Taylor polynomial of unknown function by known data set.
We obtained a system of equations by substituting known data set to the Taylor polynomial and found
the derivatives needed for the interpolation model using the system of equations. Then we intended to
compare the proposed method with some existing methods taking single polynomial, trigonometric
and exponential functions as test functions. Also, we compared our model with a well-known existing
method, polynomial interpolation. The proposed model overlaps on the polynomial function and
exponential function when 5 points are taken with an even comparatively larger step size. The error of
our model is less than the error of polynomial interpolation throughout the range in both cases.
However, the proposed model deviates from the test function when using a small number of feed data for
the trigonometric function. When increased the feed data, our model and the trigonometric function fall
on the same curve whereas the usual polynomial interpolation deviates much from the trigonometric
function. Consequently, we can conclude that the proposed model performs better than polynomial
interpolation for polynomial, trigonometric and exponential functions. And in the case of the increased
amount of feed data, we record improved accuracy at interpolating procedure.
