# aveknt

Provide knot averages

## Syntax

```tstar = aveknt(t,k) ```

## Description

`tstar = aveknt(t,k) `returns the averages of successive `k-1` knots, i.e., the sites

which are recommended as good interpolation site choices when interpolating from splines of order `k` with knot sequence $t={\left({t}_{i}\right)}_{i=1}^{n+k}$.

## Examples

`aveknt([1 2 3 3 3],3)` returns the vector `[2.5000 3.0000]`, while `aveknt([1 2 3],3)` returns the empty vector.

With `k` and the strictly increasing sequence `breaks` given, the statements

```t = augknt(breaks,k); x = aveknt(t); sp = spapi(t,x,sin(x)); ```

provide a spline interpolant to the sine function on the interval `[breaks(1)..breaks(end)]`.

For `sp` the B`-`form of a scalar-valued univariate spline function, and with `tstar` and `a` computed as

```tstar = aveknt(fnbrk(sp,'knots'),fnbrk(sp,'order')); a = fnbrk(sp,'coefs'); ```

the points (tstar(i), a(i)) constitute the control points of the spline, i.e., the vertices of the spline's control polygon.