A modification of krawczyk's algorithm

Abstract

A modification of Krawczyk's algorithm is proposed both in one and n-dimensional real spaces. This is done by introducing a control-factor γ which is to be determined and used only when the convergence conditions of Krawczyk's algorithm are violated. In all other cases γ is chosen as one. This means that the modified algorithm works like Krawczyk's algorithm. The main purpose of this is to make the Krawczyk's algorithm as unfailingly convergent. The convergence theorems are established to show that the rate of convergence of the modified method has been enhanced from linear to quadratic. The modified method is tested on a number of numerical examples and their results are enclosed. In almost all cases, the modified method works faster than the usual Krawczyk's method.

Keywords:

• Control-factor
• Newton's method
• quadratic convergence
• monotonicity

C.R. Categories:

• G.1.5