Some variant of Newton's method with third-order convergence
Applied Mathematics and Computation
Modified Newton's method with third-order convergence and multiple roots
Journal of Computational and Applied Mathematics
Geometric constructions of iterative functions to solve nonlinear equations
Journal of Computational and Applied Mathematics
A modified Newton method for rootfinding with cubic convergence
Journal of Computational and Applied Mathematics
A modified Newton method with cubic convergence: the multivariate case
Journal of Computational and Applied Mathematics
Letter to the Editor: Third-order modification of Newton's method
Journal of Computational and Applied Mathematics
A geometric construction of iterative functions of order three to solve nonlinear equations
Computers & Mathematics with Applications
Some modifications of Newton's method with fifth-order convergence
Journal of Computational and Applied Mathematics
A simply constructed third-order modifications of Newton's method
Journal of Computational and Applied Mathematics
A family of Newton-type methods for solving nonlinear equations
International Journal of Computer Mathematics
The cubic semilocal convergence on two variants of Newton's method
Journal of Computational and Applied Mathematics
A cubically convergent Newton-type method under weak conditions
Journal of Computational and Applied Mathematics
Some modification of Newton's method by the method of undetermined coefficients
Computers & Mathematics with Applications
Some higher-order modifications of Newton's method for solving nonlinear equations
Journal of Computational and Applied Mathematics
Some multi-step iterative methods for solving nonlinear equations
Computers & Mathematics with Applications
Iterative methods improving newton's method by the decomposition method
Computers & Mathematics with Applications
Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim
Computers & Mathematics with Applications
Hi-index | 7.30 |
Recently, there has been some progress on Newton-type methods with cubic convergence that do not require the computation of second derivatives. Weerakoon and Fernando (Appl. Math. Lett. 13 (2000) 87) derived the Newton method and a cubically convergent variant by rectangular and trapezoidal approximations to Newton's theorem, while Frontini and Sormani (J. Comput. Appl. Math. 156 (2003) 345; 140 (2003) 419 derived further cubically convergent variants by using different approximations to Newton's theorem. Homeier (J. Comput. Appl. Math. 157 (2003) 227; 169 (2004) 161) independently derived one of the latter variants and extended it to the multivariate case. Here, we show that one can modify the Werrakoon-Fernando approach by using Newton's theorem for the inverse function and derive a new class of cubically convergent Newton-type methods.