On Sat, 2008-07-12 at 20:56 +0800, Hongzheng Wang wrote: > My question is, if the function > is known only on a set of points, how can the integration be > calculated conveniently?
I may not have understood your question. But ... If you have a function f and know its values at points x_1,...,x_n only and wish to estimate the integral of f, you have two problems (1) find g to estimate f. (2) find G to estimate the integral of g. There are several possibilities for (1) depending on the circumstances. Here are three possibilities. There are more. (1) Estimate g as a piecewise linear function between x_1 and x_n. Then the integral of g is easily found without numerical integration. In this case it is not even necessary to find g explicitly. (2) Estimate g using cubic splines. Then, again, the integral of g can be found without numerical integration. (3) Estimate g using some more complex regression model. Depending on the model, you may or may not be able to find the integral of g explicitly. If not, you can use numerical integration methods on g. -- JDL _______________________________________________ Help-gsl mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-gsl
