Quadratic Interpolation Algorithm for Minimizing Tabulated Function
E.A. Youness, S.Z. Hassan and Y.A. El-Rewaily
DOI : 10.3844/jmssp.2008.217.221
Journal of Mathematics and Statistics
Volume 4, Issue 4
Problem statement: The problem of finding the minimum value of objective function, when we know only some values of it, is needed in more practical fields. Quadratic interpolation algorithms are the famous tools deal with this kind of these problems. These algorithms interested with the polynomial space in which the objective function is approximated. Approach: In this study we approximated the objective function by a one dimensional quadratic polynomial. This approach saved the time and the effort to get the best point at which the objective is minimized. Results: The quadratic polynomial in each one of the steps of the proposed algorithm, accelerate the convergent to the best value of the objective function without taking into account all points of the interpolation set. Conclusion: Any n-dimensional problem of finding a minimal value of a function, given by some values, can be converted to one dimensional problem easier in deal.
© 2008 E.A. Youness, S.Z. Hassan and Y.A. El-Rewaily. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.