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Test Problem.

Use your routines to compute the Gaussian integral

whose value (computed with 14 accurate digits) is shown above.

The results are given below.

 SINGLE PRECISION Tol Trapezoidal Simpson error n error n 0.1E+01 -.2E-01 0.5E-03 0.1E+00 -.2E-01 0.4E-04 0.1E-01 -.1E-02 0.4E-04 0.1E-02 -.3E-03 0.4E-04 0.1E-03 -.2E-04 0.3E-05 0.1E-04 -.1E-05 0.2E-06 0.1E-05 -.2E-06 -.8E-07 0.1E-06 -.2E-06 0.0E+00 0.1E-07 -.1E-04 0.8E-07 0.1E-08 -.1E-04 0.8E-07 0.1E-09 -.1E-04 0.8E-07 0.1E-10 -.1E-04 0.8E-07 0.1E-11 -.1E-04 0.8E-07

 DOUBLE PRECISION TOL Trapezoidal Simpson error n error n 0.1E+01 -.2E-01 0.5E-03 0.1E+00 -.2E-01 0.4E-04 0.1E-01 -.1E-02 0.4E-04 0.1E-02 -.3E-03 0.4E-04 0.1E-03 -.2E-04 0.3E-05 0.1E-04 -.1E-05 0.2E-06 0.1E-05 -.3E-06 0.1E-07 0.1E-06 -.2E-07 0.7E-09 0.1E-07 -.1E-08 0.7E-09 0.1E-08 -.3E-09 0.4E-10 0.1E-09 -.2E-10 0.3E-11 0.1E-10 -.1E-11 0.2E-12 0.1E-11 -.3E-12 0.6E-14

Aside from the project, compare the results above with thre results obtained via Gaussian Quadrature integration formula. This method gives excellent results with only several node points; it is therefore much more efficient than both trapezoidal and Simpson rules.

 Gauss Quadrature error n -3.0E-4 2 -1.2E-5 3 4.4E-7 4 -8.0E-9 5

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