[Scilab-users] Monotone preserving splin

[fujimoto2005]

Dear Buruno,

I see the situation.
Suppose the number of the sub-interbal is n-1 ( that is
[x1.x2],[x2,x3],...,[xn-1,xn]).
The number of unknown variables of sub-cubic polynomials is 4n-4.
When "spline_type" is "not_a_knot","clamped"or "periodic" ,we have 4n-4
constraints as follows.
2n-2 for data matching and continuity.
n-2 for the first derivatives and comtinuity at x2,...,xn-1.
n-2 for the second derivatives and continuity at x2,...,xn-1.
2 for the derivative values at near the end points which the above
"spline_type" gives.

When "spline_type" is "monotone", the constaraits are as follows.
2n-2 for data mathing and continuity.
2n-2 for the first deribatives mathing and continuity at xi and xi+1 on
sub-interval(i=1,...,n-1).
These derivatives are calculated by the finite difference method.

Best regards.



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