On Newton-type methods with cubic convergence
From MaRDI portal
Publication:1763661
DOI10.1016/j.cam.2004.07.027zbMath1063.65037OpenAlexW1966502208MaRDI QIDQ1763661
Publication date: 22 February 2005
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2004.07.027
Newton methodIterative methodsNewton-type methodcubic convergenceNumerical examplesNonlinear equationsNewton theoremRootfindingInverse function
Related Items
Unnamed Item ⋮ Larger convergence regions for an efficient two-step iterative method ⋮ New modification methods for finding zeros of nonlinear functions ⋮ Higher order Traub-Steffensen type methods and their convergence analysis in Banach spaces ⋮ Semilocal Convergence Theorem for a Newton-like Method ⋮ Semilocal convergence analysis of a fifth-order method using recurrence relations in Banach space under weak conditions ⋮ A general class of one-parametric with memory method for solving nonlinear equations ⋮ A third-order convergent iterative method for solving non-linear equations ⋮ Extension of Murakami's high-order non-linear solver to multiple roots ⋮ On a Newton-type method under weak conditions with dynamics ⋮ Iterative methods for nonlinear systems associated with finite difference approach in stochastic differential equations ⋮ Local convergence analysis of a modified Newton-Jarratt's composition under weak conditions ⋮ Newton‐like iteration methods for solving non‐linear equations ⋮ Unnamed Item ⋮ A new family of generalized quadrature methods for solving nonlinear equations ⋮ Several new third-order and fourth-order iterative methods for solving nonlinear equations ⋮ A family of Newton-type methods for solving nonlinear equations ⋮ The improvements of Chebyshev-Halley methods with fifth-order convergence ⋮ A one parameter square root family of two-step root-finders ⋮ Some third-order families of iterative methods for solving nonlinear equations ⋮ Convergence of a class of efficient quadrature-based predictor-corrector methods for root-finding ⋮ Third-order modification of Newton's method ⋮ Derivative free iterative methods for nonlinear systems ⋮ An infinite family of one-step iterators for solving nonlinear equations to increase the order of convergence and a new algorithm of global convergence ⋮ Iterative methods with fourth-order convergence for nonlinear equations ⋮ The improvements of modified Newton's method ⋮ A one-parameter fourth-order family of iterative methods for nonlinear equations ⋮ Construction of third-order modifications of Newton's method ⋮ Multipoint iterative method with cubic convergence ⋮ Eighth order family of iterative methods for nonlinear equations and their basins of attraction ⋮ Aitken type methods with high efficiency ⋮ Construction of Newton-like iteration methods for solving nonlinear equations ⋮ On the construction of iterative methods with at least cubic convergence ⋮ A two-parameter third-order family of methods for solving nonlinear equations ⋮ New family of iterative methods for nonlinear equations ⋮ Third-order iterative methods free from second derivatives for nonlinear equation ⋮ Increasing the order of convergence for iterative methods to solve nonlinear systems ⋮ A modification of Newton method with third-order convergence ⋮ Modified secant-type methods for unconstrained optimization ⋮ Some modification of Newton's method by the method of undetermined coefficients ⋮ New iterations of \(R\)-order four with reduced computational cost ⋮ A Steffensen-like method and its higher-order variants ⋮ Chaos and convergence of a family generalizing Homeier's method with damping parameters ⋮ Three-step iterative methods for nonlinear equations ⋮ An analysis of the properties of the variants of Newton's method with third order convergence ⋮ Some iterative schemes for nonlinear equations ⋮ An iterative method with cubic convergence for nonlinear equations ⋮ New techniques to develop higher order iterative methods for systems of nonlinear equations ⋮ A note on some recent methods for solving nonlinear equations ⋮ Newton-Kantorovich convergence theorem of a modified Newton's method under the gamma-condition in a Banach space ⋮ Means based modifications of Newton's method for solving nonlinear equations ⋮ Improved iterative methods for solving nonlinear equations ⋮ A splitting method to solve a single nonlinear equation with derivative-free iterative schemes ⋮ An optimal and efficient general eighth-order derivative free scheme for simple roots ⋮ Choosing the most stable members of Kou's family of iterative methods ⋮ A third-order Newton-type method to solve systems of nonlinear equations ⋮ New iterative schemes for nonlinear equations ⋮ A family of composite fourth-order iterative methods for solving nonlinear equations ⋮ Solving nonsmooth equations using family of derivative-free optimal methods ⋮ A new modified secant-like method for solving nonlinear equations ⋮ Sixth-order modifications of Newton's method based on Stolarsky and Gini means ⋮ An efficient family of optimal fourth-order iterative methods for finding multiple roots of nonlinear equations ⋮ Family of Cubically Convergent Schemes Using Inverse Newton Function for Multiple Roots ⋮ Multidimensional Homeier's generalized class and its application to planar 1D Bratu problem ⋮ Local convergence analysis of an efficient fourth order weighted-Newton method under weak conditions ⋮ Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions ⋮ Convergence analysis of a three step Newton-like method for nonlinear equations in Banach space under weak conditions ⋮ Two new classes of optimal Jarratt-type fourth-order methods ⋮ Zero-finder methods derived using Runge-Kutta techniques ⋮ A new modified King-Werner method for solving nonlinear equations ⋮ Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim ⋮ Iteration methods with an auxiliary function for nonlinear equations ⋮ Composite Fourth Order Newton Type Method for Simple Root ⋮ A simply constructed third-order modification of Newton's method ⋮ On new third-order convergent iterative formulas ⋮ A geometric construction of iterative functions of order three to solve nonlinear equations ⋮ A cubically convergent Newton-type method under weak conditions ⋮ The cubic semilocal convergence on two variants of Newton's method ⋮ Local convergence of an optimal eighth order method under weak conditions ⋮ On some improved harmonic mean Newton-like methods for solving systems of nonlinear equations ⋮ Higher order iterative schemes for nonlinear equations using decomposition technique ⋮ From third to fourth order variant of Newton's method for simple roots ⋮ A class of efficient quadrature-based predictor-corrector methods for solving nonlinear systems ⋮ Achieving higher order of convergence for solving systems of nonlinear equations ⋮ Local convergence of a Newton-Traub composition in Banach spaces ⋮ An improvement to double-step Newton method and its multi-step version for solving system of nonlinear equations and its applications ⋮ A method for obtaining iterative formulas of order three ⋮ On some cubic convergence iterative formulae without derivatives for solving nonlinear equations ⋮ Some higher-order modifications of Newton's method for solving nonlinear equations ⋮ Some modifications of Newton's method with fifth-order convergence ⋮ Efficient three-step iterative methods with sixth order convergence for nonlinear equations ⋮ A family of iterative methods with accelerated eighth-order convergence ⋮ A geometric construction of iterative formulas of order three ⋮ Note on a cubically convergent Newton-type method under weak conditions ⋮ Several new third-order iterative methods for solving nonlinear equations ⋮ On modified Newton methods with cubic convergence ⋮ A new third-order Newton-type iterative method for solving nonlinear equations ⋮ Some multi-step iterative methods for solving nonlinear equations ⋮ A new method of secant-like for nonlinear equations ⋮ Some variants of Chebyshev-halley methods free from second derivative ⋮ Fourth-order variants of Cauchy's method for solving non-linear equations ⋮ Certain improvements of Newton's method with fourth-order convergence ⋮ The construction of rational iterative methods for solving nonlinear equations ⋮ How to increase convergence order of the Newton method to \(2\times m\)? ⋮ New third-order method for solving systems of nonlinear equations ⋮ Interval methods with fifth order of convergence for solving nonlinear scalar equations ⋮ Adams-like techniques for zero-finder methods ⋮ Two-point generalized Hermite interpolation: double-weight function and functional recursion methods for solving nonlinear equations ⋮ Two optimal families of iterative methods for solving nonlinear equations ⋮ Local convergence of a family of weighted-Newton methods ⋮ Accelerating the convergence speed of iterative methods for solving nonlinear systems ⋮ Families of Newton-like methods with fourth-order convergence ⋮ Some class of third- and fourth-order iterative methods for solving nonlinear equations ⋮ A new Jarratt-type fourth-order method for solving system of nonlinear equations and applications ⋮ Iterative methods improving Newton's method by the decomposition method
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Modified Newton's method with third-order convergence and multiple roots
- Geometric constructions of iterative functions to solve nonlinear equations
- A modified Newton method for rootfinding with cubic convergence.
- Some variant of Newton's method with third-order convergence.
- A modified Newton method with cubic convergence: the multivariate case
- A variant of Newton's method with accelerated third-order convergence