New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 A new family of eighth-order derivative-free methods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight.
Rajinder Thukral
doaj +2 more sources
A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem [PDF]
Applied Mathematics and Computation, 2014 A derivative-free optimal eighth-order family of iterative methods for solving nonlinear equations is constructed using weight functions approach with divided first order differences.
Carlos Andreu +3 more
semanticscholar +4 more sources
Derivative-free Methods for Structural Optimization
eCAADe proceedings, 2018 The focus on efficiency has grown over recent years, and nowadays it is critical that buildings have a good performance regarding different criteria. This need prompts the usage of algorithmic approaches, analysis tools, and optimization algorithms, to ...
Guilherme Ilunga, A. Leitão
semanticscholar +2 more sources
An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros [PDF]
Mathematics, 2021 In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α
Ramandeep Behl +3 more
doaj +2 more sources
Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods [PDF]
Abstract and Applied Analysis, 2012 Optimization problems defined by (objective) functions for which derivatives are unavailable or available at an expensive cost are emerging in computational science.
F. Soleymani, S. Shateyi
doaj +2 more sources
Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations
European Journal of Mathematical Analysis, 2023 In nonlinear problems where function’s derivatives are difficult or expensive to compute, derivative-free iterative methods are good options to find the numerical solution.
Sunil Kumar +3 more
doaj +1 more source
Scalable subspace methods for derivative-free nonlinear least-squares optimization [PDF]
Mathematical programming, 2021 We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular we prove high-
C. Cartis, Lindon Roberts
semanticscholar +1 more source
On the adaptive selection of the parameter in stabilized finite element approximations [PDF]
, 2013 A systematic approach is developed for the selection of the stabilization parameter for stabilized finite element approximation of the Stokes problem, whereby the parameter is chosen to minimize a computable upper bound for the error in the approximation.
Rankin, Richard Andrew Robert +3 more
core +4 more sources
A New Derivative-Free Method to Solve Nonlinear Equations
Mathematics, 2021 A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated.
Beny Neta
doaj +1 more source
Extended Seventh Order Derivative Free Family of Methods for Solving Nonlinear Equations
Mathematics, 2023 A plethora of applications from Computational Sciences can be identified for a system of nonlinear equations in an abstract space. These equations are mostly solved with an iterative method because an analytical method does not exist for such problems ...
Ramandeep Behl +3 more
doaj +1 more source