Methods of Numerical Integration

By Luc Bauwens, M. Lubrano, Jean-François Richard. 2000

1,651 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/271d99612211715659ca68f145117bd9ad16e75c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

In Mechanical Engineering

Citations in the corpus

Residual Networks as Flows of Diffeomorphisms (2019, background): “Higher-order explicit schemes, for instance the classic fourth-order Runge-Kutta scheme, seem of great interest as well as implicit integration schemes [8].”
A general database of hydrometeor single scattering properties at microwave and sub-millimetre wavelengths (2018, positive): “The later case is handled by Romberg integration (Davis and Rabinowitz, 1984).”
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation (2006, methodology): “An efficient approach for infinite integrals with exponentially decaying integrand is GaussLaguerre quadrature [5].”
Some New Perspectives on the Method of Control Variates (2002, positive): “The key to the idea is to take advantage of the fact that a closely related integrand can be analytically integrated; see [5], p.”
Fast Construction of the Fejér and Clenshaw–Curtis Quadrature Rules (2006, methodology): “The explicit expressions for the weights considered are summarized by Davis and Rabinowitz [2]: the weights w k , w f2 k of Fejér’s rules are given in Equs.”
Dimension–Adaptive Tensor–Product Quadrature (2003, background): “Patterson and Gauß–Legendre formulas [7].”
Interpolation and Approximation by Polynomials (2003, background): “See, for example, Davis and Rabinowitz [11].”
AutoInt: Automatic Integration for Fast Neural Volume Rendering (2020, methodology): “Conventionally, the VRE is computed numerically by Riemann sums, quadratures, or Monte-Carlo methods [11], whose accuracy thus largely depends on the number of samples taken along the ray.”
Is Gauss Quadrature Better than Clenshaw-Curtis? (2008, background): “They can also be found in monographs on numerical integration, including Davis and Rabinowitz (1967, 1975, and 1984), Brass (1977), Engels (1980), Evans (1993), Krommer and Ueberhuber (1998), and Kythe and Schäferkotter (2005) [6, 12, 18, 19, 40, 41].”
Asymptotic efficiency of the two-stage estimation method for copula-based models (2005, methodology): “3)with continuousmarginsand 1, 2, beingscalars, theelementsof I and V are straightforward to compute using two-dimensional numerical integration [2].”
Linear barycentric rational quadrature (2012, methodology): “The slopes of the curves reflect the experimental order 4 of the composite Simpson rule for sufficiently large n [13] and the order 6 of the composite Boole rule.”
Rotational velocities of A-type stars. III. Velocity distributions (2006, methodology): “These operations are carried on using the smoothed distributions and overlapping parabolas integration method (Davis & Rabinowitz 1984).”
A Numerical-Integration Perspective on Gaussian Filters (2006, background): “The resulting multiple integration formula is a product rule [33], [34].”
On the Global Error of Discretization Methods for Highly-Oscillatory Ordinary Differential Equations (2002, background): “Superior performance can be ex-pected, for example, from Filon quadrature (Davis & Rabinowitz 1984) or other tech-niques for highly-oscillatory integrands.”
Lie-group methods (2000, background): “This is hardly surprising, since even the estimation of the error of univariate Gauss–Legendre quadrature is difficult (Davis and Rabinowitz 1984).”
Sparse Gauss-Hermite Quadrature Filter with Application to Spacecraft Attitude Estimation (2011, background): “Theorem 3.1 [34]: Assume that the sequence of univariate quadrature rules I fIi : i 2 Ng is defined such that Ii is exact for all univariate polynomials of the order up to 2i 1.”