Semi-Local Convergence of Iterative Methods and Banach Space Valued Functions in Abstract Fractional Calculus [PDF]
Revue d'analyse numérique et de théorie de l'approximation, 2018 We present a semi-local convergence analysis for a class of iterative methods under generalized conditions. Some applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.
George Anastassiou +1 more
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Unified Semi-Local Convergence for k—Step Iterative Methods With Flexible and Frozen Linear Operator [PDF]
Mathematics, 2018 The aim of this article is to present a unified semi-local convergence analysis for a k-step iterative method containing the inverse of a flexible and frozen linear operator for Banach space valued operators. Special choices of the linear operator reduce the method to the Newton-type, Newton’s, or Stirling’s, or Steffensen’s, or other methods.
Santhosh George +1 more
exaly +5 more sources
Improved semi-local convergence of the Gauss-Newton method for systems of equations
Journal of Mathematical Sciences and Modelling, 2018 Our new technique of restricted convergence domains is employed to provide a finer convergence analysis of the Gauss-Newton method in order to solve a certain class of systems of equations under a majorant condition. The advantages are obtained under the
Santhosh George, İoannis K Argyros
doaj +4 more sources
Extended convergence analysis of Newton-Potra solver for equations [PDF]
Journal of Numerical Analysis and Approximation Theory, 2020 In the paper a local and a semi-local convergence of combined iterative process for solving nonlinear operator equations is investigated. This solver is built based on Newton solver and has R-convergence order 1.839....
Ioannis Argyros +3 more
doaj +8 more sources
Compensating Operator and Weak Convergence of Semi-Markov Process to the Diffusion Process without Balance Condition [PDF]
Journal of Applied Mathematics, 2015 Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes.
Igor V. Malyk
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Journal of Computational and Applied Mathematics, 2015 A semi-local analysis of Newton's method for solving nonlinear inclusion problems in Banach space is presented in this paper. Under a affine majorant condition on the nonlinear function which is associated to the inclusion problem, the robust convergence of the method and results on the convergence rate are established.
O P Ferreira
exaly +4 more sources
Local and semi-local convergence analysis of a multi-step method [PDF]
Electronic Journal of MathematicsIoannis K. Argyros +3 more
doaj +2 more sources
SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION [PDF]
Surveys in Mathematics and its Applications, 2020 The article is about the analysis of semi-local convergence of a seventh-order iterative method used for finding the roots of a nonlinear equation in Banach spaces.
Neha Gupta, Jai Prakash Jaiswal
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On the Semi-Local Convergence of an Ostrowski-Type Method for Solving Equations [PDF]
Symmetry, 2021 Symmetries play a crucial role in the dynamics of physical systems. As an example, microworld and quantum physics problems are modeled on principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Then, these equations can be solved using iterative methods.
Christopher I. Argyros +4 more
openaire +2 more sources
On the Semi-Local Convergence of a Traub-Type Method for Solving Equations [PDF]
Foundations, 2022 The celebrated Traub’s method involving Banach space-defined operators is extended. The main feature in this study involves the determination of a subset of the original domain that also contains the Traub iterates. In the smaller domain, the Lipschitz constants are smaller too.
Samundra Regmi +3 more
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