Adaptive Quadrature—Revisited

By W. Gander, Walter Gautschi. 2000

436 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mechanical Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ffcf044e511ff056d104ac89bec946583063572b

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In Control and Systems Engineering

In Mechanical Engineering

In Numerical Analysis

Citations in the corpus

Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, background): “In adaptive integration schemes [48], the point-singularity that lies inside the finite element is resolved by recursively subdividing the element into nonconforming subcells until a prescribed error tolerance is achieved.”
Probabilistic fatigue life prediction using an equivalent initial flaw size distribution (2009, methodology): “Numerical integration is performed using an adaptive recursive Simpson’s rule [33].”
Autoregressive Energy Machines (2019, methodology): “This approach exploits the fast parallel computation of the energy net, allowing us to saturate the domain of integration, and compensate for the shortcomings of the trapezoidal rule compared to more advanced adaptive quadrature methods (Gander & Gautschi, 2000).”
Optimal Fourier Inversion in Semi-Analytical Option Pricing (2007, positive): “In terms of practical reliability and robustness it therefore seems more appropriate to follow the lead by Kahl and Jäckel [KJ05] and use an adaptive numerical integration scheme such as the adaptive Gauss-Lobatto scheme developed by Gander and Gautschi [GG00].”
Vectorized adaptive quadrature in MATLAB (2008, background): “That is why the examples of [8,9] give integrands an artificial value of zero at singular points.”
Probabilistic forecasting from ensemble prediction systems: Improving upon the best‐member method by using a different weight and dressing kernel for each member (2006, methodology): “Kurtosis, as estimated by recursive adaptive Simpson quadrature using the MATLAB function quad (Gander and Gautschi 2000), is very close to β2 = 5.”
Numerical Cubature on Scattered Data by Radial Basis Functions (2005, methodology): “An explicit expression of FW2(θ) can be obtained by integrating directly ΨW2(a/ cos θ) with Matlab/Symbolic FW2(θ) = a2 84c6 { 8a5s + 10a5sc2 + 15a5sc4 + 15a5c6 log ((1 + s)/c) − 42a4sc −56a4sc3 − 112a4sc5 + 84a3sc2 + 126a3sc4 + 126a3c6 log ((1 + s)/c) −70a2sc3 − 140a2sc5 + 42sc5 } , where s = sin θ”
A high‐precision model of first‐order reversal curve (FORC) functions for single‐domain ferromagnets with uniaxial anisotropy (2005, methodology): “The integral is evaluated using adaptive Gauss/Lobatto quadrature [Gander and Gautschi, 2000] with a relative accuracy of 10 6 or better.”
Improved streamlines and time-of-flight for streamline simulation on irregular grids (2007, methodology): “We have used a Lobatto quadrature [21] with a tolerance of 10−6.”
Continuous Flow Driven Inversion for Arterial Spin Labeling Using Pulsed Radiofrequency and Gradient Fields (2008, neutral): “01 using the recursive adaptive Simpson quadrature algorithm (26).”
Three-dimensional analysis of scattering losses due to sidewall roughness in microphotonic waveguides (2005, methodology): “The integration of the radiation profile of each mode [see (17)] was performed using an adaptive Lobotto quadrature [20].”