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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
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Axioms, 2021 We develop a local convergence of an iterative method for solving nonlinear least squares problems with operator decomposition under the classical and generalized Lipschitz conditions. We consider the case of both zero and nonzero residuals and determine
Ioannis K. Argyros +4 more
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Computational Divided Differencing and Divided-Difference Arithmetics [PDF]
, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Reps, Thomas W., Rall, Louis B.
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ON DIVIDED-DIFFERENCE SEMIGROUPS [PDF]
International Journal of Algebra and Computation, 2011 The Newtonian divided-difference operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations.
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On one generalization of Wronskian
Lietuvos Matematikos Rinkinys, 2007 In this article the properties of the specially introduced determinant, elements of which are the divided differences in different orders are studied.
Eduardas Kirjackis
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Generalized Iterative Method of Order Four with Divided Differences
Foundations, 2023 Numerous applications from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert, or Banach, to mention a few.
Samundra Regmi +2 more
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Local convergence for composite Chebyshev-type methods
Communications in Advanced Mathematical Sciences, 2018 We replace Chebyshev's method for solving equations requiring the second derivative by a Chebyshev-type second derivative free method. The local convergence analysis of the new method is provided using hypotheses only on the first derivative in contrast ...
Santhosh George, İoannis K Argyros
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Mathematics, 2019 We study an iterative differential-difference method for solving nonlinear least squares problems, which uses, instead of the Jacobian, the sum of derivative of differentiable parts of operator and divided difference of nondifferentiable parts. Moreover,
Ioannis Argyros +2 more
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Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions
Computation, 2020 The technique of using the restricted convergence region is applied to study a semilocal convergence of the Newton−Kurchatov method. The analysis is provided under weak conditions for the derivatives and the first order divided differences ...
Ioannis K. Argyros +2 more
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The tests of the belonging of functions to the classes Fn(D) and Qn(D)
Lietuvos Matematikos Rinkinys, 2021 In the work with the aid of the divided and finite differences are introduced classes Fn(D) and Qn(D) of functions holomorphic in region D. Different properties of functions from these classes are studied, the tests of the belonging of functions to the ...
Jevgenijus Kirjatskis +1 more
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