Results 11 to 20 of about 347 (48)
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 39, Page 2487-2499, 2003., 2003 Recently, Tautenhahn and Hämarik (1999) have considered a monotone rule as a parameter choice strategy for choosing the regularization parameter while considering approximate solution of an ill‐posed operator equation Tx = y, where T is a bounded linear operator between Hilbert spaces.
Santhosh George, M. Thamban Nair
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An iterative approach to a constrained least squares problem
Abstract and Applied Analysis, Volume 2003, Issue 8, Page 503-512, 2003., 2003 A constrained least squares problem in a Hilbert space H is considered. The standard Tikhonov regularization method is used. In the case where the set of the constraints is the nonempty intersection of a finite collection of closed convex subsets of H, an iterative algorithm is designed.
Simeon Reich, Hong-Kun Xu
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Stable Approximations of a Minimal Surface Problem with Variational Inequalities
Abstract and Applied Analysis, Volume 2, Issue 1-2, Page 137-161, 1997., 1997 In this paper we develop a new approach for the stable approximation of a minimal surface problem associated with a relaxed Dirichlet problem in the space BV(Ω) of functions of bounded variation. The problem can be reformulated as an unconstrained minimization problem of a functional 𝒥 on BV(Ω) defined by 𝒥(u) = 𝒜(u) + ∫∂Ω|Tu − Φ|, where 𝒜(u) is the ...
M. Zuhair Nashed, Otmar Scherzer
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To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case [PDF]
, 2013 In parametric equations - stochastic equations are a special case - one may want to approximate the solution such that it is easy to evaluate its dependence of the parameters.
Giraldi, Loïc +5 more
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Stable discretization methods with external approximation schemes
International Journal of Stochastic Analysis, Volume 8, Issue 4, Page 405-413, 1995., 1995 We investigate the external approximation‐solvability of nonlinear equations‐ an upgrade of the external approximation scheme of Schumann and Zeidler [3] in the context of the difference method for quasilinear elliptic differential equations.
Ram U. Verma
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On iterative solution of nonlinear functional equations in a metric space
International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 1, Page 161-170, 1983., 1983 Given that A and P as nonlinear onto and into self‐mappings of a complete metric space R, we offer here a constructive proof of the existence of the unique solution of the operator equation Au = Pu, where u ∈ R, by considering the iterative sequence Aun+1 = Pun (u0 prechosen, n = 0, 1, 2, …).
Rabindranath Sen, Sulekha Mukherjee
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Semilocal analysis of equations with smooth operators
International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 3, Page 553-563, 1981., 1981 Recent work on semilocal analysis of nonlinear operator equations is informally reviewed. A refined version of the Kantorovich theorem for Newton′s method, with new error bounds, is presented. Related topics are briefly surveyed.
George J. Miel
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Matkowski theorems in the context of quasi-metric spaces and consequences on G-metric spaces
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 In this paper, we prove the characterization of a Matkowski's theorem in the setting of quasi-metric spaces.
Karapιnar Erdal +2 more
doaj +1 more source
A data-driven iteratively regularized Landweber iteration
, 2020 We derive and analyse a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems.
Aspri, Andrea +3 more
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Strong Convergence Theorems for Nonexpansive Mappings by Viscosity Approximation Methods in Banach Spaces [PDF]
, 2008 In this paper, we introduce a modified Ishikawa iterative process for a pair of nonexpansive mappings and obtain a strong convergence theorem in the framework of uniformly Banach spaces. Our results improve and extend the recent ones announced by Kim and
Qin, Xiaolong, Su, Yongfu, Wu, Changqun
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