The Experts below are selected from a list of 134181 Experts worldwide ranked by ideXlab platform
Chiencheng Tseng - One of the best experts on this subject based on the ideXlab platform.
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design of digital integrator using stancu polynomial and Numerical Integration rules
International Symposium on Communications and Information Technologies, 2010Co-Authors: Chiencheng Tseng, Suling LeeAbstract:In this paper, the design of digital integrator is investigated. First, the Stancu polynomial is described. Then, non-integer delay sample estimation of discrete-time sequence is derived by using Stancu polynomial. Next, the Numerical Integration rules and non-integer delay sample estimation are applied to obtain the transfer function of digital integrator. Finally, some Numerical comparisons with conventional digital integrators are made to demonstrate the effectiveness of this new design approach.
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closed form design of digital iir integrators using Numerical Integration rules and fractional sample delays
IEEE Transactions on Circuits and Systems, 2007Co-Authors: Chiencheng TsengAbstract:In this paper, the Numerical Integration rules and fractional sample delays will be used to obtain the closed-form design of infinite-impulse response (IIR) digital integrators. There are two types of Numerical Integration rules to be investigated. One is Newton-Cotes quadrature rule, the other is Gauss-Legendre Integration rule. Although the proposed IIR digital integrators will involve the implementation of fractional sample delays, this problem is easily solved by applying well-documented design techniques of the finite-impulse response Lagrange and IIR allpass fractional delay filters. Several design examples are illustrated to demonstrate the effectiveness of the proposed method
Qinghui Zhang - One of the best experts on this subject based on the ideXlab platform.
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Numerical Integration in Galerkin meshless methods, applied to elliptic Neumann problem with non-constant coefficients
Advances in Computational Mathematics, 2011Co-Authors: Qinghui Zhang, Uday BanerjeeAbstract:In this paper, we explore the effect of Numerical Integration on the Galerkin meshless method used to approximate the solution of an elliptic partial differential equation with non-constant coefficients with Neumann boundary conditions. We considered Galerkin meshless methods with shape functions that reproduce polynomials of degree k ≥ 1. We have obtained an estimate for the energy norm of the error in the approximate solution under the presence of Numerical Integration. This result has been established under the assumption that the Numerical Integration rule satisfies a certain discrete Green’s formula, which is not problem dependent, i.e., does not depend on the non-constant coefficients of the problem. We have also derived Numerical Integration rules satisfying the discrete Green’s formula.
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effect of Numerical Integration on meshless methods
Computer Methods in Applied Mechanics and Engineering, 2009Co-Authors: Ivo Babuska, Uday Banerjee, John E Osborn, Qinghui ZhangAbstract:Abstract In this paper, we present the effect of Numerical Integration on meshless methods with shape functions that reproduce polynomials of degree k ⩾ 1 . The meshless method was used on a second order Neumann problem and we derived an estimate for the energy norm of the error between the exact solution and the approximate solution from the meshless method under the presence of Numerical Integration. This estimate was obtained under the assumption that the Numerical Integration scheme satisfied a form of Green’s formula. We also indicated how to obtain Numerical Integration schemes satisfying this property.
Francoisxavier Briol - One of the best experts on this subject based on the ideXlab platform.
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bayesian probabilistic Numerical Integration with tree based models
Neural Information Processing Systems, 2020Co-Authors: Harrison Zhu, Xing Liu, Ruya Kang, Zhichao Shen, Seth Flaxman, Francoisxavier BriolAbstract:Bayesian quadrature (BQ) is a method for solving Numerical Integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP) approximation of the integrand. As a result, BQ is inherently limited to cases where GP approximations can be done in an efficient manner, thus often prohibiting very high-dimensional or non-smooth target functions. This paper proposes to tackle this issue with a new Bayesian Numerical Integration algorithm based on Bayesian Additive Regression Trees (BART) priors, which we call BART-Int. BART priors are easy to tune and well-suited for discontinuous functions. We demonstrate that they also lend themselves naturally to a sequential design setting and that explicit convergence rates can be obtained in a variety of settings. The advantages and disadvantages of this new methodology are highlighted on a set of benchmark tests including the Genz functions, and on a Bayesian survey design problem.
Harrison Zhu - One of the best experts on this subject based on the ideXlab platform.
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bayesian probabilistic Numerical Integration with tree based models
Neural Information Processing Systems, 2020Co-Authors: Harrison Zhu, Xing Liu, Ruya Kang, Zhichao Shen, Seth Flaxman, Francoisxavier BriolAbstract:Bayesian quadrature (BQ) is a method for solving Numerical Integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP) approximation of the integrand. As a result, BQ is inherently limited to cases where GP approximations can be done in an efficient manner, thus often prohibiting very high-dimensional or non-smooth target functions. This paper proposes to tackle this issue with a new Bayesian Numerical Integration algorithm based on Bayesian Additive Regression Trees (BART) priors, which we call BART-Int. BART priors are easy to tune and well-suited for discontinuous functions. We demonstrate that they also lend themselves naturally to a sequential design setting and that explicit convergence rates can be obtained in a variety of settings. The advantages and disadvantages of this new methodology are highlighted on a set of benchmark tests including the Genz functions, and on a Bayesian survey design problem.
Frank W Nijhoff - One of the best experts on this subject based on the ideXlab platform.
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Closed-form modified Hamiltonians for integrable Numerical Integration schemes
Nonlinearity, 2018Co-Authors: Shami A Alsallami, Jitse Niesen, Frank W NijhoffAbstract:Modified Hamiltonians are used in the field of geometric Numerical Integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually diverges. In contrast, this paper constructs and analyzes explicit examples of nonlinear systems where the modified Hamiltonian has a closed-form expression and hence converges. These systems arise from the theory of discrete integrable systems. We present cases of one- and two-degrees symplectic mappings arising as reductions of nonlinear integrable lattice equations, for which the modified Hamiltonians can be computed in closed form. These modified Hamiltonians are also given as power series in the time step by Yoshida's method based on the Baker-Campbell-Hausdorff series. Another example displays an implicit dependence on the time step which could be of relevance to certain implicit schemes in Numerical analysis. In the light of these examples, the potential importance of integrable mappings to the field of geometric Numerical Integration is discussed.
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Closed-form modified Hamiltonians for integrable Numerical Integration schemes
'IOP Publishing', 2018Co-Authors: Alsallami Sam, Niesen J, Frank W NijhoffAbstract:Modified Hamiltonians are used in the field of geometric Numerical Integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually diverges. In contrast, this paper constructs and analyzes explicit examples of nonlinear systems where the modified Hamiltonian has a closed-form expression and hence converges. These systems arise from the theory of discrete integrable systems. We present cases of one- and twodegrees symplectic mappings arising as reductions of nonlinear integrable lattice equations, for which the modified Hamiltonians can be computed in closed form. These modified Hamiltonians are also given as power series in the time step by Yoshida’s method based on the Baker–Campbell–Hausdorff series. Another example displays an implicit dependence on the time step which could be of relevance to certain implicit schemes in Numerical analysis. In light of these examples, the potential importance of integrable mappings to the field of geometric Numerical Integration is discussed
