CONSTRUCTION OF A NEW FAMILY OF EFFICIENT IMBEDDED POLYNOMIALS WITH DISTINCT COEFFICIENTS

Abstract

We propose a new family of multi-purpose imbedded polynomials having distinct coefficients. There exist relationships between various coefficients of the members of the family, which considerably reduce the computational cost of development as well as using any number of members of the family in a particular problem. Every member polynomial of degree n going through (n+1) focuses {(xi, yi): i=0,1….......n} can be constructed very easily from another member having degree (n-1). In this paper, it is shown that the family of polynomials M exists and is efficient, reliable and more accurate as compared to other available techniques. The family has been successfully applied to the problem of interpolation in this paper. Therefore, the family M is also called the Malik‘s Imbedded Interpolating Polynomials (M.I.I.P). The family M gives similar results as compared to Lagrange Interpolation as for as accuracy is concerned but they are more efficient. The proposed polynomials are more efficient, more stable and more reliable as compared to other traditional interpolation methods due to remarkable reduction in mathematical operations. Our approach and the design of the method is different of available methods of prototype interpolation Methods. We have considered the drawbacks of other methods and eliminated from our approach. The superiority of the family is established and reported.