## Some new variants of Newton’s method.(English)Zbl 1065.65067

The paper is devoted to the study of some hybrid Newton-type methods of the form $x_{n+1}=x_n-\frac{f(x_n)}{E(f,x_n)},$ where $$E(f,x_n)$$ is either $$\frac{2f'(x_n)f'(z_{n+1})}{f'(x_n)+f'(z_{n+1})}$$ or $$f'((x_n+x_{n+1})/2)$$, with $z_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}.$

### MSC:

 65H05 Numerical computation of solutions to single equations
Full Text:

### References:

 [1] Weerakoon, S; Fernando, T.G.I, A variant of Newton’s method with accelerated third-order convergence, Appl. math. lett., 13, 8, 87-93, (2000) · Zbl 0973.65037 [2] Ford, W.F; Pennline, J.A, Accelerated convergence in Newton’s method, SIAM review, 38, 658-659, (1996) · Zbl 0863.65026 [3] Gerlach, J, Accelerated convergence in Newton’s method, SIAM review n]36, 272-276, (1994) · Zbl 0814.65046 [4] Wait, R, The numerical solution of algebraic equations, (1979), John Wiley & Sons · Zbl 0403.65007 [5] Igarashi, M, A termination criterion for iterative methods used to find the zeros of polynomials, Math. comp., 42, 165-171, (1984) · Zbl 0529.65022
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.