Results 21 to 30 of about 228,877 (212)
Extended High Order Algorithms for Equations under the Same Set of Conditions
Algorithms, 2021 A variety of strategies are used to construct algorithms for solving equations. However, higher order derivatives are usually assumed to calculate the convergence order.
Ioannis K. Argyros +5 more
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Applications of ball spaces theory: fixed point theorems in semimetric spaces and ball convergence
Journal of Fixed Point Theory and Applications, 2022 AbstractIn the paper, we apply some of the results from the theory of ball spaces in semimetric setting. This allows us to obtain fixed point theorems which we believe to be unknown to this day. As a byproduct, we obtain the equivalence of some different notions of completeness in semimetric spaces where the distance function is 1-continuous.
Piotr Nowakowski, Filip Turoboś
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Basics of a generalized Wiman-Valiron theory for monogenic Taylor series of finite convergence radius [PDF]
, 2010 In this paper, we develop the basic concepts for a generalized Wiman-Valiron theory for Clifford algebra valued functions that satisfy inside an n + 1-dimensional ball the higher dimensional Cauchy-Riemann system . These functions are called monogenic or
Constales, Denis +2 more
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Taylor expansions and Castell estimates for solutions of stochastic differential equations driven by rough paths [PDF]
, 2020 We study the Taylor expansion for the solutions of differential equations driven by $p$-rough paths with $p>2$. We prove a general theorem concerning the convergence of the Taylor expansion on a nonempty interval provided that the vector fields are ...
Feng, Qi, Zhang, Xuejing
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3D ball skinning using PDEs for generation of smooth tubular surfaces [PDF]
, 2010 We present an approach to compute a smooth, interpolating skin of an ordered set of 3D balls. By construction, the skin is constrained to be C-1 continuous, and for each ball, it is tangent to the ball along a circle of contact.
Brian Whited +10 more
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Improved convergence ball and error analysis of Müller's method
Boletim da Sociedade Paranaense de Matemática, 2022 We present an improved convergence analysis of Müller's method for solving nonlinear equation under conditions that the divided differences of order one of the involved function satisfy the Lipschitz conditions. Our result improves the earlier work in literature. Numerical examples are presented to illustrate the theoretical results.
Ioannis K. Argyros +2 more
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Ball Convergence for Higher Order Methods Under Weak Conditions
Journal of Mathematical Study, 2021 We present a local convergence analysis for higher order methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies, Taylor expansions and hypotheses on higher order Fréchet-derivatives are used. We expand the applicability of these methods using only hypotheses on the first Fréchet derivative.
Ioannis K. Argyros, Santhosh George
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Distributed Solution of Large-Scale Linear Systems via Accelerated Projection-Based Consensus [PDF]
, 2017 Solving a large-scale system of linear equations is a key step at the heart of many algorithms in machine learning, scientific computing, and beyond. When the problem dimension is large, computational and/or memory constraints make it desirable, or even ...
Avestimehr, Salman +3 more
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Ball Convergence for eighth order method
, 2017 Consider the problem of approximating a locally unique solution x of the nonlinear equation F(x) = 0, (21.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space X with values in a Banach space Y. The equation (21.1) covers wide range of problems in classical analysis and applications [1-30]. Closed form solutions
Argyros, Ioannis K +1 more
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Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3D ball [PDF]
, 2013 We establish new global well-posedness results along Gibbs measure evolution for the nonlinear wave equation posed on the unit ball in $\mathbb{R}^3$ via two distinct approaches.
Bourgain, Jean, Bulut, Aynur
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