Novel hybrid algorithms for root determining using advantages of open methods and bracketing methods

Abstract

There are two numerical approaches for root determining methods: open methods and bracketing methods. Open methods usually converge much more quickly than the bracketing methods, but they may diverge in some cases. Bracketing methods always converge but they are slow compared to the open methods. In this paper, two novel blended algorithms are proposed. These algorithms have advantages of the bracketing methods and the open methods. In particular, the first hybrid algorithm consists of false-position method with modified secant method (FP-MSe) and the second blended algorithm consists of false-position method with trigonometric secant method (FP-TMSe). The numerical results show that the proposed algorithms overcome bisection (Bi) and false-position (FP) methods. On the other hand, the presented algorithms overcome the trisection (Tri), secant (Se) and Newton- Raphson (NR) algorithms according to the iteration number and the average of running time. Finally, the implementation results show the superiority of the proposed algorithms on other related algorithms.