## Variants of Newton’s method using fifth-order quadrature formulas.(English)Zbl 1122.65350

Summary: Some variants of Newton’s method are developed in this work in order to solve nonlinear equations depending on one or several variables, based in rules of quadrature of fifth order. We prove the third or fifth order of convergence of these methods for dimension one, and the second or third order in several variables, depending on the behaviour of the second derivative. Moreover, different numeric tests confirm or improve theoretic results and allow us to compare these variants with Newton’s classical method.

### MSC:

 65H10 Numerical computation of solutions to systems of equations
Full Text:

### References:

 [1] Weerakoon, S.; Fernando, T.G.I., A variant of newton’s method with accelerated third-order convergence, Applied mathematics letters, 13, 8, 87-93, (2000) · Zbl 0973.65037 [2] Ortega, J.M.; Rheinboldt, W.C., Iterative solution of nonlinear equations in several variables, (1970), Academic Press, Inc. · Zbl 0241.65046 [3] Traub, J.F., Iterative methods for the solution of equations, (1982), Chelsea Publishing Company New York · Zbl 0472.65040 [4] Ozban, A.Y., Some new variants of newton’s method, Applied mathematics letters, 17, 677-682, (2004) · Zbl 1065.65067 [5] Gerlach, J., Accelerated convergence in newton’s method, SIAM review, 36, 2, 272-276, (1994) · Zbl 0814.65046 [6] Cordero, A.; Torregrosa, J.R., Variants of newton’s method for functions of several variables, Applied mathematics and computation, 183, 199-208, (2006) · Zbl 1123.65042
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.