An Adaptive Computer Algorithm Using Newly Developed Imbedded Interpolating Polynomials to Determine the Equations of Polynomials and Their Derivatives
Journal Title: LAHORE GARRISON UNIVERSITY RESEARCH JOURNAL OF COMPUTER SCIENCE AND INFORMATION TECHNOLOGY - Year 2017, Vol 1, Issue 3
Abstract
The problem of generalization of certain principles and rules in Science, Engineering, Economics and all other disciplines dominates; particularly when these schemes are required to be expressed in mathematical functions or polynomial. The adaptive computer algorithm finds and displays the equations of polynomials of various degrees passing through given set of coordinate points: 𝑥 [ ],𝑦[ ]. The automatic Adaptive Algorithm interpolates and uses a newly developed imbedded family of polynomial, having coefficients of higher degree computable using the coefficients of lowers degree polynomials. Apart from determining the equations of polynomials in classical algebraic form, the adaptive computer algorithm implemented in C++, computes the equations of function passing through these points as well as the equations of differentiated polynomials for various orders. The user need to enter the point through which the polynomial passes, rest will be the responsibility of the adaptive algorithm. The Adaptive Algorithm converts the Data into Polynomial in the classicalalgebraic form and then proceeds to compute the desired derivate of first or higher order. The algorithm handles Equally Spaced Data as well as Unequally Spaced Data. The superiority of the proposed method is established as compared to other existing methods
Authors and Affiliations
AFTAB AHMAD MALIK, MUJTABA ASAD, WAQAR AZEEM
Keywords
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