Theory and Modern Applications
Table 1 Root-mean-square errors for classical Gamma operators and newly constructed Gamma operators with \(\mu =0.25 \) for different values of n, test function \(f(x)=x^{\log (1+x)} \), on an equally spaced 10000 evaluation grid
n | RMS Error for \(G_{n}(f;x)\) | RMS Error for \(\varGamma _{n}^{\mu } ( f;x ) \) |
|---|---|---|
1 | 6.402506e–01 | 2.202781e–02 |
5 | 2.846635e–01 | 5.771027e–03 |
10 | 9.328952e–02 | 2.756072e–03 |
20 | 6.356742e–02 | 1.305979e–03 |
30 | 2.464479e–02 | 8.495264e–04 |
40 | 1.747821e–02 | 6.284498e–04 |