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In mathematics and numerical analysis, the van Wijngaarden transformation is a variant on the Euler transform used to accelerate the convergence of an alternating series.
One algorithm to compute Euler's transform runs as follows:
Compute a row of partial sums
Adriaan van Wijngaarden's contribution was to point out that it is better not to carry this procedure through to the very end, but to stop two-thirds of the way. If a 0 , a 1 , … , a 12 {\displaystyle a_{0},a_{1},\ldots ,a_{12}} are available, then s 8 , 4 {\displaystyle s_{8,4}} is almost always a better approximation to the sum than s 12 , 0 {\displaystyle s_{12,0}}. In many cases the diagonal terms do not converge in one cycle so process of averaging is to be repeated with diagonal terms by bringing them in a row. This process of successive averaging of the average of partial sum can be replaced by using the formula to calculate the diagonal term.