Error Bounds for Optimal Definite Quadrature Formulae
Journal of Approximation Theory, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kohler, P., Nikolov, G.
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Random search algorithm for solving the nonlinear Fredholm integral equations of the second kind. [PDF]
PLoS ONE, 2014 In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind.
Zhimin Hong, Zaizai Yan, Jiao Yan
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Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis
, 2015 The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating distribution by
Tanaka, Ken'ichiro, Toda, Alexis Akira
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A Multilevel Heterogeneous ADMM Algorithm for Elliptic Optimal Control Problems with L1-Control Cost
Mathematics, 2023 In this paper, elliptic optimal control problems with L1-control cost and box constraints on the control are considered. To numerically solve the optimal control problems, we use the First optimize, then discretize approach.
Xiaotong Chen +3 more
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On an Optimal Quadrature Formula for Classes of Functions Given by Modulus of Continuity
Моделирование и анализ информационных систем, 2014 The problem of minimizing the error of a cubature formula on the classes of functions given by modulus of continuity for cubature formulas with fixed nodes on the boundary of gird rectangular localization domain of nodes is considered.
M. Sh. Shabozov
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Elementary test for non-classicality based on measurements of position and momentum
, 2015 We generalise a non-classicality test described by Kot et al. [Phys. Rev. Lett. 108, 233601 (2010)], which can be used to rule out any classical description of a physical system.
Borregaard, Johannes +2 more
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Uniqueness of the Optimal Nodes of Quadrature Formulae [PDF]
Mathematics of Computation, 1981 We prove the uniqueness of the quadrature formula with minimal error in the space W ~ q r [ a , b ] , 1 > q > ∞ \tilde W_q^r[a,b],1 > q > \infty , of
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Construction of Supplemental Functions for Direct Serendipity and Mixed Finite Elements on Polygons
Mathematics, 2023 New families of direct serendipity and direct mixed finite elements on general planar, strictly convex polygons were recently defined by the authors. The finite elements of index r are H1 and H(div) conforming, respectively, and approximate optimally to ...
Todd Arbogast, Chuning Wang
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On optimal quadrature formulae
Journal of Inequalities and Applications, 2000 For integrals involving a nonnegative weight function on a finite interval the author proposes a procedure to construct quadrature formulas which are exact for solutions of linear differential equations and are optimal in the sense of Sard. The author establishes necessary and sufficient conditions for the existence of such formulas.
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Weighted Optimal Quadrature Formulas in Sobolev Space and Their Applications
AlgorithmsThe optimization of computational algorithms is one of the main problems of computational mathematics. This optimization is well demonstrated by the example of the theory of quadrature and cubature formulas.
Kholmat Shadimetov, Khojiakbar Usmanov
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