Table 1 The values of the maximum deviations and Lebesgue constants for sets \(\pmb{\breve{T} }\) , \(\pmb{\hat{T} }\) , and \(\pmb{X^{*}}\)
From: Lebesgue functions and Lebesgue constants in polynomial interpolation
n | set \(\boldsymbol {\breve{T}}\) | set \(\boldsymbol {\hat{T}}\) | set \(\boldsymbol {X^{*}}\) | ||
|---|---|---|---|---|---|
\(\boldsymbol {\delta _{n} (\breve{T})}\) | \(\boldsymbol {\Lambda _{n} (\breve{T})}\) | \(\boldsymbol {\delta _{n} (\hat{T})}\) | \(\boldsymbol {\Lambda _{n} (\hat{T})}\) | \(\boldsymbol {\Lambda _{n} (X^{*} )}\) | |
10 | 0.050 781 | 2.056 087 | 0.019 471 | 2.068 744 | 2.051 706 |
20 | 0.056 995 | 2.463 129 | 0.019 340 | 2.479 193 | 2.460 788 |
40 | 0.061 827 | 2.887 067 | 0.018 952 | 2.904 441 | 2.885 809 |