Third-order methods from quadrature formulae for solving systems of nonlinear equations
- 1 February 2004
- journal article
- Published by Elsevier BV in Applied Mathematics and Computation
- Vol. 149 (3), 771-782
- https://doi.org/10.1016/s0096-3003(03)00178-4
Abstract
We extend to p-dimensional problems a modification of the Newton method, based on quadrature formulas of order at least one, which produces iterative methods with order of convergence three. A general error analysis providing the higher order of convergence is given. These new methods may be more efficient then other third-order methods as they do not require the use of the second-order Fréchet derivative.Keywords
This publication has 8 references indexed in Scilit:
- Modified Newton's method with third-order convergence and multiple rootsJournal of Computational and Applied Mathematics, 2003
- Some variant of Newton’s method with third-order convergenceApplied Mathematics and Computation, 2002
- Kepler equation and accelerated Newton methodJournal of Computational and Applied Mathematics, 2002
- A variant of Newton's method with accelerated third-order convergenceApplied Mathematics Letters, 2000
- Accelerated Convergence in Newton’s MethodSiam Review, 1996
- A note on the convergence of Halley's method for solving operator equationsThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1995
- Accelerated Convergence in Newton’s MethodSiam Review, 1994
- Methodus nova accurata & facilis inveniendi radices æqnationum quarumcumque generaliter, sine praviæ reductionePhilosophical Transactions of the Royal Society of London, 1694