Van Wijngaarden transformation

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 s 0 , k = ∑ n = 0 k ( − 1 ) n a n {\displaystyle s_{0,k}=\sum _{n=0}^{k}(-1)^{n}a_{n}} and form rows of averages between neighbors s j + 1 , k = s j , k + s j , k + 1 2 {\displaystyle s_{j+1,k}={\frac {s_{j,k}+s_{j,k+1}}{2}}} The first column s j , 0 {\displaystyle s_{j,0}} then contains the partial sums of the Euler transform.

Source: Wikipedia — Van Wijngaarden transformation (CC BY-SA 4.0)

Van Wijngaarden transformation

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 s 0 , k = ∑ n = 0 k ( − 1 ) n a n {\displaystyle s_{0,k}=\sum _{n=0}^{k}(-1)^{n}a_{n}} and form rows of averages between neighbors s j + 1 , k = s j , k + s j , k + 1 2 {\displaystyle s_{j+1,k}={\frac {s_{j,k}+s_{j,k+1}}{2}}} The first column s j , 0 {\displaystyle s_{j,0}} then contains the partial sums of the Euler transform.

Source: Wikipedia "Van Wijngaarden transformation" · CC BY-SA 4.0

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