Results 31 to 40 of about 2,749,932 (104)
CONSTRUCTION OF OPTIMAL QUADRATURE FORMULAS IN SOBOLEV SPACE.
, 2023 In this article, a series of problems related to the creation and application of quadrature and cubature formulas, including: finding errors of quadrature and cubature formulas in the Gilbert phases of differential functions; calculating error functionals of found extremal functions using extremal functions; finding the conditions for the existence and
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New quadrature formulas from conformal maps
, 2008 Gauss and Clenshaw-Curtis quadrature, like Legendre and Chebyshev spectral methods, make use of grids strongly clustered at boundaries. From the viewpoint of polynomial approximation this seems necessary and indeed in certain respects optimal ...
Lloyd N. Trefethen, Nicholas Hale
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Optimal Quadrature Formulas for the Sobolev Space $H^1$
, 2016 We study optimal quadrature formulas for arbitrary weighted integrals and integrands from the Sobolev space $H^1([0,1])$. We obtain general formulas for the worst case error depending on the nodes $x_j$. A particular case is the computation of Fourier coefficients, where the oscillatory weight is given by $ρ_k(x) = \exp(- 2 πi k x)$.
Zhang, Shun, Novak, Erich
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Quadrature formulas based on rational interpolation
, 1993 We consider quadrature formulas based on interpolation using the basis functions 1 / ( 1 + t k x ) ( k =
Ingrid Vanherwegen, Walter Van Assche
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Optimal designs for 3D shape analysis with spherical harmonic descriptors [PDF]
We determine optimal designs for some regression models which are frequently used for describing 3D shapes. These models are based on a Fourier expansion of a function defined on the unit sphere in terms of spherical harmonic basis functions.
Dette, Holger +2 more
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Multilevel quadrature formulae for the optimal control of random PDEs
Numerische MathematikAbstract This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal control problems discretized with different levels of accuracy of the physical and ...
Nobile, Fabio, Vanzan, Tommaso
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Generalized averaged Gaussian quadrature and applications [PDF]
, 2019 A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate ...
Spalević, Miodrag
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Newton-Cotes Quadrature Formulas
, 2011 This Demonstration shows the Newton–Cotes quadrature formulas of integration and their application to the integration of sin(x)Componente Curricular::Educação Superior::Ciências Exatas e da Terra ...
Sevilla, Eugenio Bravo
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Quadrature formulas obtained by variable transformation and the DE-rule
, 1985 This paper gives a survey of the results known to date about quadrature formulas obtained by variable transformation followed by an application of the trapezoidal rule with an equal mesh size.
Mori, Masatake
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