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".

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