The Experts below are selected from a list of 4242 Experts worldwide ranked by ideXlab platform
Nenad Ujevic - One of the best experts on this subject based on the ideXlab platform.
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a corrected Quadrature Formula and applications
Anziam Journal, 2008Co-Authors: Nenad Ujevic, A J RobertsAbstract:A straightforward three-point Quadrature Formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the Quadrature Formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite Formulas can be applied to integrands with lower order derivatives.
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error inequalities for an optimal Quadrature Formula
Journal of Applied Mathematics and Computing, 2007Co-Authors: Nenad UjevicAbstract:An optimal 3-point Quadrature Formula of closed type is derived. It is shown that the optimal Quadrature Formula has a better error bound than the well-known Simpson's rule. A corrected Formula is also considered. Various error inequalities for these Formulas are established. Applications in numerical integration are given.
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error inequalities for an optimal 2 point Quadrature Formula of open type
Inequality theory and applications. Vol. 4, 2007Co-Authors: Nenad UjevicAbstract:An optimal 2-point Quadrature Formula of open type is derived. It is shown that this Formula has better error bound than the well-known 2-point Gauss Formula. Various error inequalities for this Formula are established. Applications in numerical integration are given.
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a corrected Quadrature Formula and applications
arXiv: Numerical Analysis, 2003Co-Authors: Nenad Ujevic, A J RobertsAbstract:A straightforward 3-point Quadrature Formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the Quadrature Formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite Formulas can be applied to integrands with lower order derivatives.
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error inequalities for a Quadrature Formula of open type
Revista colombiana de matemáticas, 2003Co-Authors: Nenad UjevicAbstract:An optimal 2-point Quadrature Formula of open type is derived. It is shown that the optimal Quadrature Formula has a better error bound than the well-known 2-point Gauss Quadrature Formula. Various error inequalities for this Formula are established. Applications in numerical integration are given.
B. M. Kwak - One of the best experts on this subject based on the ideXlab platform.
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Robust design with arbitrary distributions using Gauss-type Quadrature Formula
Structural and Multidisciplinary Optimization, 2009Co-Authors: W Chen, B. M. KwakAbstract:In this paper, we present the Gauss-type Quadrature Formula as a rigorous method for statistical moment estimation involving arbitrary input distributions and further extend its use to robust design optimization. The mathematical background of the Gauss-type Quadrature Formula is introduced and its relation with other methods such as design of experiments (DOE) and point estimate method (PEM) is discussed. Methods for constructing one dimensional Gauss-type Quadrature Formula are summarized and the insights are provided. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed for two different multi-dimensional integration methods, the tensor product Quadrature (TPQ) Formula and the univariate dimension reduction (UDR) method. Through several examples, it is shown that the Gauss-type Quadrature Formula can be effectively used in robust design involving various non-normal distributions. The proposed design sensitivity analysis significantly reduces the number of function calls of robust optimization using the TPQ Formulae, while using the UDR method, the savings of function calls are observed only in limited situations.
W Chen - One of the best experts on this subject based on the ideXlab platform.
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Robust design with arbitrary distributions using Gauss-type Quadrature Formula
Structural and Multidisciplinary Optimization, 2009Co-Authors: W Chen, B. M. KwakAbstract:In this paper, we present the Gauss-type Quadrature Formula as a rigorous method for statistical moment estimation involving arbitrary input distributions and further extend its use to robust design optimization. The mathematical background of the Gauss-type Quadrature Formula is introduced and its relation with other methods such as design of experiments (DOE) and point estimate method (PEM) is discussed. Methods for constructing one dimensional Gauss-type Quadrature Formula are summarized and the insights are provided. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed for two different multi-dimensional integration methods, the tensor product Quadrature (TPQ) Formula and the univariate dimension reduction (UDR) method. Through several examples, it is shown that the Gauss-type Quadrature Formula can be effectively used in robust design involving various non-normal distributions. The proposed design sensitivity analysis significantly reduces the number of function calls of robust optimization using the TPQ Formulae, while using the UDR method, the savings of function calls are observed only in limited situations.
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robust structural optimization using gauss type Quadrature Formula
Transactions of The Korean Society of Mechanical Engineers A, 2009Co-Authors: Sanghoon Lee, Kiseog Seo, Shikui Chen, W ChenAbstract:In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type Quadrature Formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type Quadrature Formula are constructed from the input probability distributions and utilized in the construction of multidimensional Quadrature Formula such as the tensor product Quadrature (TPQ) Formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.
Borislav Bojanov - One of the best experts on this subject based on the ideXlab platform.
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Quadrature Formula for computed tomography
Journal of Approximation Theory, 2010Co-Authors: Borislav Bojanov, Guergana PetrovaAbstract:We give a bivariate analog of the Micchelli-Rivlin Quadrature for computing the integral of a function over the unit disk using its Radon projections.
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uniqueness of the gaussian interval Quadrature Formula
Numerische Mathematik, 2003Co-Authors: Borislav Bojanov, Petar PetrovAbstract:We prove that for a given finite interval [a, b] and any set of preassigned non-negative numbers h 1 ,?,h n such that h 1 +a?+h n
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gaussian interval Quadrature Formula
Numerische Mathematik, 2001Co-Authors: Borislav Bojanov, Petar PetrovAbstract:We prove the existence of a Gaussian Quadrature Formula for Tchebycheff systems, based on integrals over non-overlapping subintervals of arbitrary fixed lengths and the uniqueness of this Formula in the case the subintervals have equal lengths.
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numerical integration over a disc a new gaussian Quadrature Formula
Numerische Mathematik, 1998Co-Authors: Borislav Bojanov, Guergana PetrovaAbstract:We construct a Quadrature Formula for integration on the unit disc which is based on line integrals over $n$ distinct chords in the disc and integrates exactly all polynomials in two variables of total degree $2n-1$ .
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on a Quadrature Formula of micchelli and rivlin
Journal of Computational and Applied Mathematics, 1996Co-Authors: Borislav BojanovAbstract:Abstract Micchelli and Rivlin (1972) obtained a Quadrature Formula of highest algebraic degree of precision for the Fourier-Chebyshev coefficients A n ( f ), which is based on the divided differences of f ′ at the zeros of the Chebyshev polynomial T n ( x ). We give here a simple approach to questions of this type, which applies to the coefficients in arbitrary orthogonal expansion of f . As an auxiliary result we obtain a new interpolation Formula and a new representation of the Turan Quadrature Formula.
A. I. Zadorin - One of the best experts on this subject based on the ideXlab platform.
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Modification of the Euler Quadrature Formula for functions with a boundary-layer component
Computational Mathematics and Mathematical Physics, 2014Co-Authors: A. I. ZadorinAbstract:The Euler Quadrature Formula for the numerical integration of functions with a boundary-layer component on a uniform grid is investigated. If the function under study has a rapidly growing component, the error can be significant. A uniformly accurate Quadrature Formula is constructed by modifying the Hermite interpolation Formula so that the resulting one is exact for the boundary-layer component. An analogue of the Euler Formula that is exact for the boundary-layer component is constructed. It is proved that the resulting composite Quadrature Formula is third-order accurate in space uniformly with respect to the boundary-layer component and its derivatives.
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Quadrature Formula with five nodes for functions with a boundary layer component
International Conference on Numerical Analysis and Its Applications, 2012Co-Authors: A. I. Zadorin, Nikita ZadorinAbstract:Quadrature Formula for one variable functions with a boundary layer component is constructed and studied. It is assumed that the integrand can be represented as a sum of regular and boundary layer components. The boundary layer component has high gradients, therefore an application of Newton-Cotes Quadrature Formulas leads to large errors. An analogue of Newton-Cotes rule with five nodes is constructed. The error of the constructed Formula does not depend on gradients of the boundary layer component. Results of numerical experiments are presented.