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Improve break sequence distribution
Syntax
newbreaks = newknt(pp,newl) [newbreaks,distfn] = newknt(pp,newl)
Description
newknt returns the break sequence that cuts the basic interval of pp into newl pieces in such a way that a certain piecewise linear monotone function (whose ppform is returned in distfn if requested) related to the high derivative of pp is equidistributed.
The intent is to choose a break sequence suitable to the fine approximation of a function f whose rough approximation in pp is assumed to contain enough information about f to make this feasible.
Examples
See the last part of the demodifeqdem for an illustration.
Algorithm
This is the Fortran routineNEWNOT in PGS. With k the order of the pp function f in pp, the function |Dkf| is approximated by a piecewise constant function obtained by local, discrete, differentiation of the variation of Dk-1f. The new break sequence is chosen to subdivide the basic interval of the pp f in such a way that See Also
difeqdem