Example
As an example, the Gaussian function is integrated from 0 to 1, i.e. the error function erf(1) ≈ 0.842700792949715. The triangular array is calculated row by row and calculation is terminated if the two last entries in the last row differ less than 10−8.
0.77174333 0.82526296 0.84310283 0.83836778 0.84273605 0.84271160 0.84161922 0.84270304 0.84270083 0.84270066 0.84243051 0.84270093 0.84270079 0.84270079 0.84270079The result in the lower right corner of the triangular array is accurate to the digits shown. It is remarkable that this result is derived from the less accurate approximations obtained by the trapezium rule in the first column of the triangular array.
Read more about this topic: Romberg's Method
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