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Provide knot averages


tstar = aveknt(t,k)


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

ti*:=(ti+1++ti+k1)/(k1),   i=1:n

which are recommended as good interpolation site choices when interpolating from splines of order k with knot sequence t=(ti)i=1n+k.


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.

See Also

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