On Fibonacci search method with k-Lucas numbers

Abstract

In this paper, using k-Lucas numbers instead of conventional Fibonacci numbers and conventional Lucas numbers, we have made more improvements on location of the intervals containing optimal point in the classical Fibonacci search algorithm. For that aim, using a well known test function in Optimization Theory, a computer program was developed in MAPLE to examine this idea. It was shown that the our method is giving better results than the previous method in the sense that converging the optimal point more rapidly.