An improvement of the Jarratt method

A Six-Order Method for Non-Linear Equations to Find Roots

“…Method has the efficiency index equal to 1.5651, which is better to Newton's method with efficiency index equal to 1.414 and the classical third order methods (1.442), such as Weerakoon and Fernando method, Chebyshev's method, Halley's method and Super-Halley method, fifth order method (1.495) of Kou, Li, Wang [24]. When compared with the sixth order methods of Parhi, Gupta, [20] and Kou and Li [13], proposed method behaves either similarly or better on the examples considered.…”

“…PM denotes proposed method. Kou and Li is the method [13], an improvement of Jarratt method. Gupta denotes for [20] Parhi and Gupta, A sixth order method for nonlinear equations.…”

“…It is shown there that the order of convergence of each family member is improved from four to six even though it adds one evaluation of the function at the point iterated by Jarratt's method per iteration. Kou et al [11][12][13] presented a family of new variants of Chebyshev-Halley methods and also an improvement of Jarratt method. These new methods have sixth order of convergence although they only add one evaluation of the function at the point iterated by Chebyshev-Halley method and Jarratt method.…”

Local Convergence for an Improved Jarratt-type Method in Banach Space

“…This method has been shown to be of convergence order between 5 and 6 [28,32]. The usual conditions for the semilocal convergence of these methods are (  ):…”

“…Many problems in computational sciences and other disciplines can be brought in a form like (1) using mathematical modelling [11,12,28,30]. Moreover, artificial intelligence and e-learning are topics of increasing interest in recent years.…”