A Method to Accelerate the Convergence of the Secant Algorithm. (19th November 2014) - Nijmeijer, M. J. P.
Abstract : We present an acceleration technique for the Secant method. The Secant method is a root-searching algorithm for a general functionf . We exploit the fact that the combination of two Secant steps leads to an improved, so-called first-order approximant of the root. The original Secant algorithm can be modified to a first-order accelerated algorithm which generates a sequence of first-order approximants. This process can be repeated: twon th order approximants can be combined in a( n + 1 ) th order approximant and the algorithm can be modified to an( n + 1 ) th order accelerated algorithm which generates a sequence of such approximants. We show that the sequence ofn th order approximants converges to the root with the same order as methods using polynomial fits off of degreen .