Lebesgue Constant
Estimates the Lebesgue constant.
lebesgue(x, refine = 4, plotting = FALSE)
x |
numeric vector of grid points |
refine |
refine the grid with |
plotting |
shall the Lebesgue function be plotted. |
The Lebesgue constant gives an estimation ||P_n f|| ≤ L ||f|| (in minimax norm) where P_n f is the interpolating polynomial of order n for f on an interval [a, b].
Lebesgue constant for the given grid points.
The Lebesgue constant plays an important role when estimating the distance of interpolating polynomials from the minimax solution (see the Remez algorithm).
Berrut, J.-P., and L. Nick Trefethen (2004). “Barycentric Lagrange Interpolation”. SIAM Review, Vol. 46(3), pp.501–517.
lebesgue(seq(0, 1, length.out = 6)) #=> 3.100425
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