[CSC 335] Your problem from homework 4

[Andrew J. Pounds]

On 10/19/13 13:31, Levi M Mitze wrote:
> Hi, Dr. Pounds.
>
> I was just reading the problem you put on the fourth homework set. Was 
> Gauss-Laguerre quadrature covered in class on Wednesday? (I missed 
> class on Wednesday.) Because I don't know what it is. I don't have it 
> anywhere in my notes except for a mention that it involves bounds of 
> integration from a constant to infinity. I can't find it in the 
> textbook either.
>
> Levi

So to use Gauss-Laguerre quadrature is defined for functions like

$\int_0^{\infty} e^{-x} f(x) dx = \sum_{i=1}^N w_i f(x_i)$

to make it so it works for a general integration you have to divide both 
sides by $e^{-x}$. In other words...


$\int_0^{\infty} f(x) dx = \sum_{i=1}^N w_i f(x_i) / e^{-x}$


$\int_0^{\infty} f(x) dx = \sum_{i=1}^N w_i f(x_i) e^{x_i}$

So for the quadrature you multiply the value of your function evaluated 
at the $x_i$ point by the exponential of $x_i$ and multiply this all by 
the weight factor $w_i$.


-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627
http://faculty.mercer.edu/pounds_aj

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/2487e269/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-5.png
Type: image/png
Size: 2609 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/2487e269/attachment-0006.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-4.png
Type: image/png
Size: 639 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/2487e269/attachment-0007.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-6.png
Type: image/png
Size: 2703 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/2487e269/attachment-0008.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-7.png
Type: image/png
Size: 2618 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/2487e269/attachment-0009.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-3.png
Type: image/png
Size: 603 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/2487e269/attachment-0010.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-2.png
Type: image/png
Size: 660 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc335/attachments/20131020/2487e269/attachment-0011.png>