Devise a quadrature formula for
f (x)dx (ie integral of f(x)dx from a to b) based on Hermit interpolation of f on the nodes x0 = a and x1 = b. Determine its degree of precision.
I would appreciate a solution so I can see how to determine the degree of precision for a question similar to one of my homework questions.
Last edited by mathematics7 (2013-04-02 17:54:03)
You want a basis using Hermite polynomials but there are at least two types of them ( maybe more, I do not know.) Which one do you want?
Also, as far as I know they are used for only one type of integral because they are orthogonal to the exponential function in it.
For this they use the physicists version. You seem to think that they can be used for the general f(x). Why do you think that?
The error term is given as:
where n is the number of points and epsilon is some point in the interval [a,b] that maximizes the error. There is also another type of error estimate that is similar to the Euler Mclaurin Summation Formula.
If you want a specific example I can run of the weights and abscissas ( zeros ).
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.