Rank: 57 based on 1089 downloads (last 30 days) and 42 files submitted

Greg von Winckel

University of New Mexico
35.069904, -106.63462

Personal Profile:

I am research associate professor at the University of New Mexico Center for High Technology Materials

Professional Interests:
PDE Constrained optimization, quantum mechanics, numerical methods


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Files Posted by Greg View all
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19 Apr 2006 Quadrature rules for spherical volume integrals Computes weights and nodes for numerically solving spherical volume integrals. Author: Greg von Winckel integration, gauss, quadrature, volume, integral, spherical 23 3
  • 5.0
5.0 | 2 ratings
27 Dec 2005 n-dimensional simplex quadrature % Construct Gauss points and weights for a n-dimensional simplex Author: Greg von Winckel integration, guass quadature, simplex, interval, triangle, tetrahedron 24 4
  • 5.0
5.0 | 4 ratings
21 Dec 2005 Gaussian Quadrature for Triangles Compute Gauss nodes and weights for a triangle Author: Greg von Winckel integration, triangle, triangular, gauss, quadrature, cubature 40 12
  • 4.4
4.4 | 10 ratings
21 Dec 2005 Gauss Quadrature for Tetrahedra Compute Gauss weights and nodes for a specied tetrahedron Author: Greg von Winckel integration, gauss quadrature, tetrahedron, tetrahedra, 3d, finite 33 3
  • 5.0
5.0 | 3 ratings
11 Nov 2005 Summed Newton-Cotes Rules 2-11 Point Summed Newton-Cotes Rules Author: Greg von Winckel integration, summed newtoncotes, numerical, uniform, grid 22 2
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13 Mar 2014 Legendre-Gauss Quadrature Weights and Nodes Computes the Legendre-Gauss weights and nodes for solving definite integrals. Author: Greg von Winckel Chao

Excellent! Thanks!

20 Dec 2013 Legendre-Gauss Quadrature Weights and Nodes Computes the Legendre-Gauss weights and nodes for solving definite integrals. Author: Greg von Winckel erick


10 Dec 2013 Fast Pentadiagonal System Solver Solves symmetric and asymmetric pentadiagonal systems. Author: Greg von Winckel jiyeon, jeon


26 Aug 2013 Pseudospectral Differentiation on an Arbitrary Grid Numerically differentiates a function on an arbitrary grid. Author: Greg von Winckel Paul O'Leary,, Matthew Harker,

It is important to point out that this approach only workd for a very small number of points (nodes). The differentiating matrix D should be rank one deficient. However running the following simple test shows that even for a very small problem D has additional nullspaces. Already with 20 nodes and quadratically spaced point the method generates a degenerate differentiating matrix.
n = 20;
% Generate a seto of linearly spaced nodes 0 <= x <= 1
x1 = linspace( 0, 1, n )';
% generate quadratically spaced nodes as an example of arbitrary
% nodes.
x2 = x1.^2;
%% Compute the Differentiating Matrices
D1 = collocD( x1 );
D2 = collocD( x2 );
%% Compute the Rank of the Matrices
% The following test shows that the matrices do not have a consistent
% rank. It may be concluded that the method, although theoritically
% sound, is serioudly deficient in its numerical behavious.
disp('Rank of the differentiating matrices');
rD1 = rank( D1 )
rD2 = rank( D2 )
% Rank deficiency
disp('Rank deficiency of the differentiating matrices');
disp('All shound be rank-1 deficient.');
rdD1 = length(x1) - rD1
rdD2 = length(x2) - rD2

19 Jun 2013 2D Barycentric Lagrange Interpolation Interpolates a function on a rectangle. Author: Greg von Winckel Alessandra

Hello! It 's the first time I write on the site. This feature I really like and I think I can be of help for the thesis I am doing. I would like to know if someone could help me to understand the inputs. What is f? xn? yn? xf? yf?
Thank you very much!

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