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pracma (version 1.9.9)

lebesgue: Lebesgue Constant

Description

Estimates the Lebesgue constant.

Usage

lebesgue(x, refine = 4, plotting = FALSE)

Arguments

x
numeric vector of grid points
refine
refine the grid with 2^refine grid points; can only be an integer between 2 and 10, default 4.
plotting
shall the Lebesgue function be plotted.

Value

Lebesgue constant for the given grid points.

Details

The Lebesgue constant gives an estimation $||P_n f|| \le L ||f||$ (in minimax norm) where $P_n f$ is the interpolating polynomial of order $n$ for $f$ on an interval $[a, b]$.

References

Berrut, J.-P., and L. Nick Trefethen (2004). ``Barycentric Lagrange Interpolation''. SIAM Review, Vol. 46(3), pp.501--517.

See Also

barylag

Examples

Run this code
lebesgue(seq(0, 1, length.out = 6))  #=> 3.100425

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