# Chebyshev points and finite difference method

• Aug 30th 2010, 06:34 AM
southsoniks
Chebyshev points and finite difference method
Hello.
I'm not a mathematician so it should not be strange that I have a problem.
I'm doing some research on interpolating polynoms.
Using the finite element method I obtained values in nodes, lets say displacements, and first used Lagrange polynomial interpolation with wich I got some polynom that behaves bad in the ends of interval.
But when I use Chebyshev points I get better results.
And here comes the problem. Finite difference has the same distance between points but Chebyshev points do not have, so the conclusion should be that it cannot be compared.
Or could they?
My question is that, could I compare this two methods? Is there any article that says how to treat finite difference with Chebyshev points.

Thanks
Best regards
• Sep 1st 2010, 12:07 AM
CaptainBlack
Quote:

Originally Posted by southsoniks
Hello.
I'm not a mathematician so it should not be strange that I have a problem.
I'm doing some research on interpolating polynoms.
Using the finite element method I obtained values in nodes, lets say displacements, and first used Lagrange polynomial interpolation with wich I got some polynom that behaves bad in the ends of interval.
But when I use Chebyshev points I get better results.
And here comes the problem. Finite difference has the same distance between points but Chebyshev points do not have, so the conclusion should be that it cannot be compared.
Or could they?
My question is that, could I compare this two methods? Is there any article that says how to treat finite difference with Chebyshev points.

Thanks
Best regards

Consider using orthogonal polynomial approximations. The give the minimum error with respect to the metric induced by the inner product that they are orthogonal with respect to.

CB
• Sep 2nd 2010, 01:18 AM
southsoniks
Thanks CB