Re: Numeric Integration of Tabulated Integrand Function: Part I
- To: mathgroup at smc.vnet.net
- Subject: [mg38418] Re: Numeric Integration of Tabulated Integrand Function: Part I
- From: Tom Burton <tburton at brahea.com>
- Date: Sat, 14 Dec 2002 03:20:04 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On 12/13/02 1:57 AM, in article atcau9$3m7$1 at smc.vnet.net, "tasande at mit.edu"
<tasande at mit.edu> wrote:
> Dear Mathemticons( * ):
>
> I have a very simple question. I have a function that is NOT specified
> as an analytic expression. Rather, the function is a previsouly
> tabulated list of the form:
>
> F( x ):=
>
> { ( x( 1 ),F( x( 1 ) ) ), ... , ( x( i ),F( x( i ) ) , ... ,
> ( x( N ),F( x( N ) ) ) }...
The choice of integration scheme is related to the best way to interpolate,
which depends on your function. But a very simple question deserves a
straightforward answer :-)
I would like to recommend that you interpolate explicitely and then
integrate. It's easy. It's pretty accurate for a lot of functions. The
method of interpolation is relatively well documented. And best of all, you
can see what you are doing. Here's an example:
data = {{1, 3}, {2, 4}, {3, 1}, {4, 2}, {5, 4}, {6, 1}, {7, 2}}
FF[x_] = Table[F[n][x_] =
Interpolation[data, InterpolationOrder -> n][x],
{n, 0, 5}]
Plot[Evaluate[FF[x]], {x, 1, 7}];
<< "NumericalMath`NIntegrateInterpolatingFunct`"
Table[{n, NIntegrateInterpolatingFunction[F[n][x], {x, 1, 7}]}, {n, 0, 5}]
Tom Burton