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NIntegrateInterpolatingFunction
As of Version 6.0, NIntegrate natively supports InterpolatingFunction objects.
gives a numerical approximation to an integral with InterpolatingFunction objects in the integrand.
gives a numerical approximation to a multidimensional integral.
更多信息
- To use
, you first need to load the Function Approximations Package using Needs["FunctionApproximations`"]. 
uses the function NIntegrate, but it breaks up the domain of integration into sections where the InterpolatingFunction objects are smooth.- If the integrand f does not contain any InterpolatingFunction objects,
is equivalent to NIntegrate. - The arguments of the InterpolatingFunction objects may themselves be univariate functions of the integration variables.
- If the integrand f is simply an InterpolatingFunction object, it is better to use Integrate because this gives a result that is exact for the polynomial approximation used in the InterpolatingFunction object.
- Numerically integrating a multidimensional integral using
with InterpolatingFunction objects containing a large number of nodes may take significantly longer than using NIntegrate. 
has the same options as NIntegrate.
范例打开所有单元
基本范例 (1)
| In[1]:= |
A trapezoidal approximation to 
:
| In[2]:= |
| Out[2]= |  |
Since 
is not smooth, NIntegrate will generate a warning message:
Using 
produces a slightly more accurate answer without any error messages:
| In[4]:= |
| Out[4]= |  |
In this case the integrand is simply an interpolating function, so you can use Integrate to check:
| In[5]:= |
| Out[5]= |  |
