1. Matlab codes for computing Gaussian Rules for Symmetric weight functions.
2. Matlab codes for computing Fejer and Clenshaw-Curtis rules for general weight functions.
3. Matlab codes for computing trigonometric quadrature rules. A comparison.
Last version: Matlab code for Gauss-like cubature over polygons [POLYGAUSS_2013_300413.zip]
Previous version: Matlab code for Gauss-like cubature over polygons [GAUSSCUB_2013.zip]. The main routine is the m. file polygauss.m. As demo, please use demo_gausscub.m. A different version, that uses less points but is more time expensive is polygaussj.m. We point out that the routines work in the GNU Octave version 2.1.73 (i686-pc-cygwin) environment. For some numerical experiments in Matlab/Octave see [readme_polygauss.pdf].
Meshless cubature from scattered data over disks and annular sectors by TPS and Green's formula [GreenDisk_v1_0a.zip]. The demo file is demoRBFsimple.m. As alternative, You can use the more complicated demoRBFcells_multiple.m that allows to subdivide the disk or annular sector into certain equal area annular sectors.
Status: correction of minor mistakes in quadrature_rules_1D.m and cubature_rules_1D.m: some indexes i in a 1D have been modified into index in the gaussian rule (that however was working in Matlab 6.1). [Last update: May 07, 2007]
Matlab code for Gauss-like cubature over spline curvilinear polygons [SPLINEGAUSS_2009.zip]. The main routine is the m. file splinegauss_2009b that performs cubature over domains with spline curvilinear boundaries.. As demo, please use demo.m for computing cubature over spline curvilinear polygons. In addition, try demo_splinegauss_moments.m for tests on computing moments w.r.t. some specific bases on such domains. All numerical experiments have been done on MAC Book, with MAC OS X, Matlab 126.96.36.1994 Release 2008a. [Latest update: November 19, 2009]. [Last update: March 27, 2009]
Padua_CC (Cubature using Padua points)
Matlab code for cubature over a square [Padua_CC.zip] (using non tensorial Padua and Morrow-Patterson Xu points). The main routine is the m. file main.m that performs cubature over a square using different formulas. All numerical experiments have been tested on Intel Centrino Duo T2400, with Windows XP, Matlab 188.8.131.520 Release 12.1 and GNU Octave 2.1.73. [Last update: October 09, 2007]
Software for Padua points interpolation and cubature. [Padua2DM.tar.gz].
ChebfunGauss: a Matlab code for Gauss-Green cubature by the Chebfun package: Matlab code that uses a suitable version of Splinegauss for bivariate domains defined analytically and approximated by Chebfuns. The files are stored in the compressed folder [CHEBFUNGAUSS_2011.zip]. For a demo use the file demo.m, for plotting cubature points plot_pts.m. [Last update: March 29, 2011]
Some routines that can be used to make experiments with WAMs can be found in the following compressed files:
- [WAM_2D_280210.zip]: a complete version that works on several bivariate domains, not easily adaptable to add own WAMs but right for experiments on general 2D domains.
- [WAM_2De_010310.zip]: a simple version that does not work on many bivariate domains, but that is easily adaptable to add 2D WAMs.
- [WAM_3D_010310.zip]: a simple version that does not work on many trivariate domains, but that is easily adaptable to add 3D WAMs.
[POLYGINT_010411.zip] contains several Matlab files for cubature/interpolation over polygons based on AFP (Approximate Fekete Points) and DLP (Discrete Leja Points). The zip file contains also Matlab routines for a minimal triangulation of a polygon and a quadrangulation of a polygon using few quadrangles and triangles. [Last Update: April 01, 2011]
LEBFEK: Matlab codes and data sets for bivariate Lebesgue and Fekete interpolation.
In M. Briani, A. Sommariva, M. Vianello, Computing Fekete and Lebesgue points: simplex, square, disk we have described some algorithms for computing (quasi-)Lebesgue and (quasi-)Fekete points on the unit simplex, a square and on the unit disk. The respective codes and sets for these domains can be found in the links below.
Computation of (almost-)minimal rules on the square.
Matlab codes for computing (almost-)minimal cubature rules on the square.
Gaussian Rules for Symmetric weight functions.
Matlab codes for computing Gaussian Rules for Symmetric weight functions.
Fejer and Clenshaw-Curtis rules for general weight functions.
Matlab codes for computing Fejer and Clenshaw-Curtis rules for general weight functions.
Matlab codes for computing trigonometric quadrature rules.
Matlab codes for computing trigonometric quadrature rules. A comparison.