Documentation |
New break distribution
newknots = newknt(f,newl)
newknt(f)
[...,distfn] = newknt(...)
newknots = newknt(f,newl) returns the knot sequence whose interior knots cut the basic interval of f into newl pieces, in such a way that a certain piecewise linear monotone function related to the high derivative of f is equidistributed.
The intent is to choose a knot sequence suitable to the fine approximation of a function g whose rough approximation in f is assumed to contain enough information about g to make this feasible.
newknt(f) uses for newl its default value, namely the number of polynomial pieces in f.
[...,distfn] = newknt(...) also returns, in distfn, the ppform of that piecewise linear monotone function being equidistributed.
If the error in the least-squares approximation sp to some data x,y by a spline of order k seems uneven, you might try for a more equitable distribution of knots by using
spap2(newknt(sp),k,x,y);
For another example, see the last part of the example "Solving an ODE by Collocation".