On Chebyshev–Halley methods with sixth-order convergence for solving non-linear equations

2007 ◽  
Vol 190 (1) ◽  
pp. 126-131 ◽  
Author(s):  
Jisheng Kou
Keyword(s):  
Linear Equations ◽  
Sixth Order ◽  
Order Convergence ◽  
Non Linear ◽  
Non Linear Equations

scholarly journals Five-point thirty-two optimal order iterative method for solving non-linear equations

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 401-409
Author(s):  
Malik Ullah ◽  
Fayyaz Ahmad
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Initial Guess ◽  
Convergence Order ◽  
Optimal Order ◽  
Order Convergence ◽  
Derivative Free ◽  
Non Linear ◽  
High Order Convergence ◽  
Non Linear Equations

A five-point thirty-two convergence order derivative-free iterative method to find simple roots of non-linear equations is constructed. Six function evaluations are performed to achieve optimal convergence order 26-1 = 32 conjectured by Kung and Traub [1]. Secant approximation to the derivative is computed around the initial guess. High order convergence is attained by constructing polynomials of quotients for functional values.

scholarly journals Basic Steffensen's Method of Higher-Order Convergence

2021 ◽  
Vol 8 (4) ◽  
pp. 184-191
Author(s):  
Ola A. Ashour
Keyword(s):  
Fourth Order ◽  
Linear Equations ◽  
Higher Order ◽  
Order Convergence ◽  
Steffensen’S Method ◽  
Non Linear ◽  
Higher Order Convergence ◽  
Non Linear Equations

In this paper, we introduce a new analog of a variant of Steffensen's method of fourth-order convergence for solving non-linear equations based on the q-deference operator.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

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