aveknt (Spline Toolbox)

Provide knot averages

Syntax

tstar = aveknt(t,k)

Description

aveknt returns the averages of successive k - 1 knots, i.e., the points

recommended as good interpolation point choices when interpolating from splines of order k with knot sequence .

Examples

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

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, with t=fnbrk(sp,'knots') and k=fnbrk(sp,'order'), the points (tstar(i), a(i)) with tstar=aveknt(t,k) constitute the vertices of the spline's control polygon.