Fundamental Journal of Mathematics and Applications, 2019 The objective of this study is to extend the usage of Newton's method for Banach space valued operators. We use our new idea of restricted convergence domain in combination with the center Lipschitz hypothesis on the Frechet-derivatives where the center is not necessarily the initial point.
IIoannis K Argyros, Santhosh GEORGE
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Gradient flows and a Trotter--Kato formula of semi-convex functions on CAT(1)-spaces [PDF]
, 2016 We generalize the theory of gradient flows of semi-convex functions on CAT(0)-spaces, developed by Mayer and Ambrosio--Gigli--Savar\'e, to CAT(1)-spaces. The key tool is the so-called "commutativity" representing a Riemannian nature of the space, and all
Ohta, Shin-ichi, Pálfia, Miklós
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Extended domain for fifth convergence order schemes
Cubo, 2021 We provide a local as well as a semi-local analysis of a fifth convergence order scheme involving operators valued on Banach space for solving nonlinear equations.
Ioannis K. Argyros, Santhosh George
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Median evidential c-means algorithm and its application to community detection [PDF]
, 2015 Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the theoretical ...
Liu, Zhun-Ga +3 more
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Extending the solvability of equations using secant-type methods in Banach space
Journal of Numerical Analysis and Approximation Theory, 2021 We extend the solvability of equations dened on a Banach space using numerically ecient secant-type methods. The convergence domain of these methods is enlarged using our new idea of restricted convergence region.
Ioannis K. Argyros, Santhosh George
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Enhancing Equation Solving: Extending the Applicability of Steffensen-Type Methods
Mathematics, 2023 Local convergence analysis is mostly carried out using the Taylor series expansion approach, which requires the utilization of high-order derivatives, not iterative methods.
Ramandeep Behl +2 more
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HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part II. Optimization of the Runge-Kutta smoother [PDF]
, 2011 Using a detailed multilevel analysis of the complete hp-Multigrid as Smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator.
Rhebergen, S., Vegt, J.J.W. van der
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Semi-local convergence of Cordero's sixth-order method
AIMS Mathematics<abstract><p>In this paper, the semi-local convergence of the Cordero's sixth-order iterative method in Banach space was proved by the method of recursion relation. In the process of proving, the auxiliary sequence and three increasing scalar functions can be derived using Lipschitz conditions on the first-order derivatives.
Xiaofeng Wang, Ning Shang
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Numerical solution of the simple Monge–Ampère equation with nonconvex dirichlet data on non-convex domains [PDF]
, 2017 The existence of a unique numerical solution of the semi-Lagrangian method for the simple Monge-Ampere equation is known independently of the convexity of the domain or Dirichlet boundary data - when the Monge-Ampere equation is posed as a Bellman ...
Jensen, Max
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A hyperbolic penalty filter method for semi-infinite programming [PDF]
, 2008 This paper presents a new reduction-type method for solving semi-infinite programming problems, where the multi-local optimization is carried out with a sequential simulated annealing algorithm, and the finite reduced problem is solved by a penalty ...
Fernandes, Edite Manuela da G. P. +1 more
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