# lebesgue: Lebesgue Constant In pracma: Practical Numerical Math Functions

## Description

Estimates the Lebesgue constant.

## Usage

 `1` ```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.

`barylag`

## Examples

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

### Example output

```[1] 3.100425
```

pracma documentation built on Dec. 11, 2021, 9:57 a.m.