Gauss-Jacobi quadrature

Weights and abscissae for radiance-to-flux conversion

Description

Ever wonder how the weights and abscissae are calculated for the numerical conversion from radiance to flux? The long and the short of it is that Gauss-Jacobi quadrature determines the weights and abscissae which is similar to Gaussian for low-point quadrature but differs substantially for high-point quadrature. This program follows Abramowitz and Stegum to produce the roots of a Jacobi polynomial from which both weights and abscissae are determined.

• MATLAB release: MATLAB 7.1.0 (R14SP3)

[John D'Errico]

If your goal is to use a gaussian quadrature, then look at
[FEX 32]. It has a complete suite of these tools, packaged together nicely.

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=32&objectType=file

If your wish is to learn how one generates a set of Gauss-Jacobi quadrature nodes and weights, then this tool may be of some help, but I felt it to be a disappointment in this respect. Not enough comments in the right places to suggest how the procedure works. It was a bit confusing to me, and I know how to build a Gauss-Jacobi rule. What files do what?

In summary, if this really were a tutorial, then have one file (heavily commented) that spells out a recurrence relationship (with references to A&S) and shows how to use it to build the appropriate polynomials. Then show how to derive the nodes and weights from these polynomials. A really useful tutorial would then give examples of the use of such a rule, perhaps in the context of a radiance to flux conversion.

[sergio garcete]

good

[abdelghani zaoui]

program of gauss-jacobi for MATLAB

[Guanghui]

 very good，but ihave some questions about it,is anyone can answer me? thanks vary much