Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
On functional iteration and the calculation of roots
ACM '61 Proceedings of the 1961 16th ACM national meeting
Maximal Order and Order of Information for Numerical Quadrature
Journal of the ACM (JACM)
n-Evaluation Conjecture for Multipoint Iterations for the Solution of Scalar Nonlinear Equations
Journal of the ACM (JACM)
Three-step iterative methods with eighth-order convergence for solving nonlinear equations
Journal of Computational and Applied Mathematics
Improving order and efficiency: Composition with a modified Newton's method
Journal of Computational and Applied Mathematics
A family of three-point methods of optimal order for solving nonlinear equations
Journal of Computational and Applied Mathematics
New eighth-order iterative methods for solving nonlinear equations
Journal of Computational and Applied Mathematics
New modifications of Potra-Pták's method with optimal fourth and eighth orders of convergence
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Three-step iterative methods with optimal eighth-order convergence
Journal of Computational and Applied Mathematics
On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency
SIAM Journal on Numerical Analysis
Constructing higher-order methods for obtaining the multiple roots of nonlinear equations
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Revisit of Jarratt method for solving nonlinear equations
Numerical Algorithms
Simply constructed family of a Ostrowski's method with optimal order of convergence
Computers & Mathematics with Applications
Accurate fourteenth-order methods for solving nonlinear equations
Numerical Algorithms
Optimal Steffensen-type methods with eighth order of convergence
Computers & Mathematics with Applications
Efficient polynomial root-refiners: A survey and new record efficiency estimates
Computers & Mathematics with Applications
Finding the solution of nonlinear equations by a class of optimal methods
Computers & Mathematics with Applications
On generalized multipoint root-solvers with memory
Journal of Computational and Applied Mathematics
Algorithm 917: Complex Double-Precision Evaluation of the Wright ω Function
ACM Transactions on Mathematical Software (TOMS)
Optimal eighth-order simple root-finders free from derivative
WSEAS Transactions on Information Science and Applications
Approximation of artificial satellites' preliminary orbits: The efficiency challenge
Mathematical and Computer Modelling: An International Journal
Regarding the accuracy of optimal eighth-order methods
Mathematical and Computer Modelling: An International Journal
On efficient two-parameter methods for solving nonlinear equations
Numerical Algorithms
On generalized biparametric multipoint root finding methods with memory
Journal of Computational and Applied Mathematics
On improved three-step schemes with high efficiency index and their dynamics
Numerical Algorithms
Calcolo: a quarterly on numerical analysis and theory of computation
Calcolo: a quarterly on numerical analysis and theory of computation
An efficient twelfth-order iterative method for finding all the solutions of nonlinear equations
Journal of Computational Methods in Sciences and Engineering
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The problem is to calculate a simple zero of a nonlinear function ƒ by iteration. There is exhibited a family of iterations of order 2n-1 which use n evaluations of ƒ and no derivative evaluations, as well as a second family of iterations of order 2n-1 based on n — 1 evaluations of ƒ and one of ƒ′. In particular, with four evaluations an iteration of eighth order is constructed. The best previous result for four evaluations was fifth order.It is proved that the optimal order of one general class of multipoint iterations is 2n-1 and that an upper bound on the order of a multipoint iteration based on n evaluations of ƒ (no derivatives) is 2n.It is conjectured that a multipoint iteration without memory based on n evaluations has optimal order 2n-1.