Small Solver Program

[Csaba Tizedes]

(02-18-2019 10:22 PM)Thomas Klemm Wrote:  

(02-18-2019 07:46 PM)Dieter Wrote:  Yes. Gamo already posted this method some time ago in the General Software Library. I have mentioned several times that the first input it NOT a guess for the root but an estimate for the function's DERIVATIVE.

You could think him stubborn.
But it made Csaba post his program which made me translate some of his papers from Hungarian to English and stumble totally unrelated upon one of his previous posts:
Quadratic fit without linear algebra (32SII) - NOT only for statistics lovers - LONG
Which I still do not understand in detail.

So all in all I'm happy with the outcome.

Cheers
Thomas

I feel myself like a star (at least for 15 minutes...)

Yes, this is my "linear regression on slope", as Chan wrote. When I was in my "Summer Practice" at a company I have modelled lots of water network flows between pump houses (sources), consumers and reservoirs, and sometimes the characteristics curves given only in paper form. Thats why I wrote this little routine.

As you can see, if the measured points has significant error, the slope will be very inaccurate then the regression also inaccurate and the coefficients can be meaningless.

But as a programming question this was an interesting "game" for me.

To the original question from Gamo: I will check carefully the lists here, but I have another idea: what if, if we just simple walking along on the function's curve until the sign is changing, then we turning back, decreasing the stepsize and walking again. If the sign of the function changed, we are turning back again, decreasing the size of the steps and so on... If the stepsize is less than a small value, we found the root.

This "marching method" not so elegant, not so fast, but good to play with it, just for a try - maybe it can be shorter than the other methods. (I have an exactly same method for finding a minimum point of a function for CASIO fx-3650P/Sencor SEC103; perfectly works, like a ball at the bottom of a hole, slowly find the deepest point, when swings around the extremum).

Csaba