R: Lebesgue Constant

lebesgue {pracma} | R Documentation

## 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.

### Details

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].

### Value

Lebesgue constant for the given grid points.

### Note

The Lebesgue constant plays an important role when estimating the distance of interpolating polynomials from the minimax solution (see the Remez algorithm).

### References

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

### See Also

`barylag`

### Examples

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

[Package pracma version 2.0.4 Index]