Results 11 to 20 of about 1,995 (109)
Journal of Complexity, 2010 The author proposes a lot of new general convergence theorems for the Picard iteration, applied to a mapping \(T\) in a complete metric space. To elaborate this new theory, he uses the concepts of quasi-homogeneous functions, gauge functions of high order, a function of initial conditions of the mapping \(T\), a convergence function of the mapping \(T\)
Petko D Proinov
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Notions of optimal transport theory and how to implement them on a computer [PDF]
, 2017 This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce mass/volume ...
Levy, Bruno, Schwindt, Erica
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The convergence theorem for fourth-order super-Halley method in weaker conditions
Journal of Inequalities and Applications, 2016 In this paper, we establish the Newton-Kantorovich convergence theorem of a fourth-order super-Halley method under weaker conditions in Banach space, which is used to solve the nonlinear equations.
Lin Zheng
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Extended Newton–Kantorovich Theorem for Solving Nonlinear Equations
Foundations, 2022 The Newton–Kantorovich theorem for solving Banach space-valued equations is a very important tool in nonlinear functional analysis. Several versions of this theorem have been given by Adley, Argyros, Ciarlet, Ezquerro, Kantorovich, Potra, Proinov, Wang, et al. This result, e.g., establishes the existence and uniqueness of the solution.
Samundra Regmi +3 more
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A numerical algorithm for $L_2$ semi-discrete optimal transport in 3D [PDF]
, 2014 This paper introduces a numerical algorithm to compute the $L_2$ optimal transport map between two measures $\mu$ and $\nu$, where $\mu$ derives from a density $\rho$ defined as a piecewise linear function (supported by a tetrahedral mesh), and where ...
Levy, Bruno
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Newton-Kantorovich convergence theorem of a new modified Halley’s method family in a Banach space [PDF]
Advances in Difference Equations, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Rongfei +4 more
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Lippmann‐Schwinger solvers for the computational homogenization of materials with pores
International Journal for Numerical Methods in Engineering, Volume 121, Issue 22, Page 5017-5041, 30 November 2020., 2020 Summary We show that under suitable hypotheses on the nonporous material law and a geometric regularity condition on the pore space, Moulinec‐Suquet's basic solution scheme converges linearly. We also discuss for which derived solvers a (super)linear convergence behavior may be obtained, and for which such results do not hold, in general.
Matti Schneider
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A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 This paper proposes a new class of difference methods with intrinsic parallelism for solving the Burgers–Fisher equation. A new class of parallel difference schemes of pure alternating segment explicit‐implicit (PASE‐I) and pure alternating segment implicit‐explicit (PASI‐E) are constructed by taking simple classical explicit and implicit schemes ...
Yueyue Pan +3 more
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Verified Error Bounds for Real Eigenvalues of Real Symmetric and Persymmetric Matrices
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 This paper mainly investigates the verification of real eigenvalues of the real symmetric and persymmetric matrices. For a real symmetric or persymmetric matrix, we use eig code in Matlab to obtain its real eigenvalues on the basis of numerical computation and provide an algorithm to compute verified error bound such that there exists a perturbation ...
Zhe Li, Xueqing Wang, Roberto Fedele
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PROJECTION-ITERATION REALIZATION OF A NEWTON-LIKE METHOD FOR SOLVING NONLINEAR OPERATOR EQUATIONS
Journal of Optimization, Differential Equations and Their Applications, 2019 We consider the problem of existence and location of a solution of a nonlinear operator equation with a Fr´echet differentiable operator in a Banach space and present the convergence results for a projection-iteration method based on a Newton-like method
Liudmyla L. Hart
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