Tracking discontinuities in hyperbolic conservation laws with spectral accuracy
Journal of Computational Physics
Vectorized adaptive quadrature in MATLAB
Journal of Computational and Applied Mathematics
Krylov deferred correction accelerated method of lines transpose for parabolic problems
Journal of Computational Physics
Meshless cubature over the disk using thin-plate splines
Journal of Computational and Applied Mathematics
Quadrature rule for Abel's equations: Uniformly approximating fractional derivatives
Journal of Computational and Applied Mathematics
Numerical Quadrature for Bessel Transformations with High Oscillations
Numerical Analysis and Its Applications
A Hybrid Fourier---Chebyshev Method for Partial Differential Equations
Journal of Scientific Computing
An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures
Journal of Computational and Applied Mathematics
Journal of Computational Physics
The application of the fluctuation expansion with extended basis set to numerical integration
WSEAS Transactions on Mathematics
The application of the fluctuation expansion with extended basis set to numerical integration
MAASE'09 Proceedings of the 2nd WSEAS international conference on Multivariate analysis and its application in science and engineering
Stable high-order quadrature rules with equidistant points
Journal of Computational and Applied Mathematics
Evaluation of the run-length distribution for a combined Shewhart-EWMA control chart
Statistics and Computing
Journal of Computational and Applied Mathematics
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
ACM Transactions on Mathematical Software (TOMS)
From numerical quadrature to Padé approximation
Applied Numerical Mathematics
Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave
Numerical Algorithms
A spectral fictitious domain method with internal forcing for solving elliptic PDEs
Journal of Computational Physics
On the Fourier Extension of Nonperiodic Functions
SIAM Journal on Numerical Analysis
Numerical solution of linear Volterra integral equations of the second kind with sharp gradients
Journal of Computational and Applied Mathematics
Weighted quadrature by change of variable
Neural, Parallel & Scientific Computations
Full length article: Computation of equilibrium measures
Journal of Approximation Theory
Journal of Computational and Applied Mathematics
Application of high order numerical quadratures to numerical inversion of the Laplace transform
Advances in Computational Mathematics
Calibrating the heston model with differential evolution
EvoCOMNET'10 Proceedings of the 2010 international conference on Applications of Evolutionary Computation - Volume Part II
Polynomial approximation of rational Bézier curves with constraints
Numerical Algorithms
Journal of Computational and Applied Mathematics
Efficient quadrature of highly oscillatory integrals with algebraic singularities
Journal of Computational and Applied Mathematics
Simulation-based optimal Bayesian experimental design for nonlinear systems
Journal of Computational Physics
Computation of integrals with oscillatory and singular integrands using Chebyshev expansions
Journal of Computational and Applied Mathematics
Interpolatory Quadrature Rules for Oscillatory Integrals
Journal of Scientific Computing
Fast construction of Fejér and Clenshaw-Curtis rules for general weight functions
Computers & Mathematics with Applications
Mathematics and Computers in Simulation
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
On the resolution power of Fourier extensions for oscillatory functions
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Pricing of early-exercise Asian options under Lévy processes based on Fourier cosine expansions
Applied Numerical Mathematics
On evaluation of Bessel transforms with oscillatory and algebraic singular integrands
Journal of Computational and Applied Mathematics
Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems
Journal of Scientific Computing
A generalized framework for nodal first derivative summation-by-parts operators
Journal of Computational Physics
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We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw-Curtis. Seven-line MATLAB codes are presented that implement both methods, and experiments show that the supposed factor-of-2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O'Hara and Smith in the 1960s, the phenomenon is explained as a consequence of aliasing of coefficients in Chebyshev expansions. Then another explanation is offered based on the interpretation of a quadrature formula as a rational approximation of $\log((z+1)/(z-1))$ in the complex plane. Gauss quadrature corresponds to Padé approximation at $z=\infty$. Clenshaw-Curtis quadrature corresponds to an approximation whose order of accuracy at $z=\infty$ is only half as high, but which is nevertheless equally accurate near $[-1,1]$.