On 9/28/19 9:26 AM, William F Pokorny wrote:
> On 9/28/19 8:08 AM, Bald Eagle wrote:
>>
>> "IGM" <iar### [at] gmailcom> wrote:
...
> 
> A site and web search might be worthwhile. I remember Tor Olav 
> Kristensen creating a simplex solver (for min, max) some while ago in 
> the SDL. Expect somebody, at some time past, has gone after a problem 
> similar to yours. Quickly finding previous work of a type can be a 
> difficult trick though.
> 

Had the thought for what you want, given you have one root/zero-crossing 
and can probable specify known values of x for lo and hi where y is 
negative and positive (or visa versa) a bisection root finder probably OK.

Here is the core of my tcl bisection root finding command:

     for {set i 0} {$i < $interationLimit} {incr i} {
        set mid  [expr {($lo + $hi)/2.0}]
        set midV [UPolyVal $mid coefList]
        if { $midV == 0.0 } {
            return [list $mid]
        } else {
            if { [expr {($loV * $midV)>=0.0}] } {
                set lo $mid
            } else {
                set hi $mid
            }
            if { [expr {($hi - $lo) < $limitVal}] } {
                return [list [expr {($lo + $hi)/2.0}]]
            }
        }
    }

    return [list];

Replace [UPolyVal $mid coefList] with your Fspline(x) evaluation while
otherwise translating the tcl into SDL and, I think, you'll be good to 
go. You might want to add a check the intersection limit was not reached 
and kick out and error in that case instead of just returning no roots 
as I do above.

Bill P.

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