Gauss-Hermite Integration Method - Keystone Mining Post

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Numerical Integration

"Numerical Integration Solutions"

Gauss-Hermite Method

N RESULT

EXACT RESULT = 0.88622692542758

(Actually after 4 is a repetition)

Results from the Gauss-Hermite method

IMPLEMENTATION
Gauss-Hermite Integration

To compute the following Gaussian integral using the Gauss-Hermite method:

I = ∫_∞^∞ e^-x² x²dx

The delegate function is simply x², since the weighting function w(x) = e^-x² for the Gauss-Hermite integration.

Running this example creates the results shown above. The exact result of this integral is equal to √π / 2. The result for n = 3 is already very close to the exact result.

Testing the Gauss-Hermite Integration Method

In order to test the Gauss-Hermite method as defined above, a new TestGaussHermite() static method has been added and executed. Supporting code and methods are not shown.

►

           static void TestGaussHermite();
              {
                 ListBox1.Items.Clear();
                 ListBox2.Items.Clear();
                 double result;
                 for (int n = 1; n < 9; n++)
                 (
                   result = Integration.GaussHermite(f4, n);
                   ListBox1.Items.Add(" " + n + );
                   ListBox2.Items.Add(" " + result);
                 )
              }