# Degree of Precision for Gaussian Quadrature scheme

• Dec 15th 2010, 05:25 PM
ductiletoaster
Degree of Precision for Gaussian Quadrature scheme
When we can freely "chose" points \$\displaystyle x_k\$ anywhere then we can optimally place them...thus we get the Gaussian Quadrature formulas.

My question is what is the Degree of Precision for Gaussian Quadrature scheme?
that uses \$\displaystyle (n+1)\$ points (n sub intervals)?

Attachment 20120

\$\displaystyle x^*_k\$ and \$\displaystyle a^*_k \$ denote the Gaussian quad points...
• Dec 15th 2010, 05:38 PM
ductiletoaster
Well I seemed to have answered my own question with a little research and some quick proof (sloppy).
But basically if u are give n points then you will have a degree of accuracy of \$\displaystyle 2n-1\$

I basically took a comparison of points version there accuracy and realized that the pattern was two times the number of points minus one....

See Link for more detail....
http://s3.amazonaws.com/cramster-res...77_n_22315.pdf

If this is wrong please let me know thanks!