Hi, Guys:

I'm using FindRoot for SOE solution,but something make me confusion. for example:



the same SOE with different variables, different result, and the second is wrong.

I think maybe I have something wrong. please help me, how to use the FindRoot?

Thanks a lot!

John

attach the file
soe.sm (6,68 KiB) scaricato 1187 volta(e).

Hi. You must to sort the variables in the same order than Unknowns.



Best regards.
Alvaro

Wrote

Hi. You must to sort the variables in the same order than Unknowns.



Best regards.
Alvaro

Hi, is there any rules for the order?



Thanks alot
John

Hi. You can't redefine Unknowns. Well, you can, but isn't the best idea. Unknowns is a function in the same plugin than FindRoots, SpecialSolvers. I don't know the internals of the plugin. My guess that the general rule is sort the variable names in lexical order, but if the name has unicode characters or some unusual ASCII character, it is best to make sure of the order to follow by evaluating Unknows(eq).

Best regards.
Alvaro.

okay， I got it. but a new question, why I can't got the result as your picture?



would you mind post the sample sm file ?

Thanks a lot!
John

Wrote

okay， I got it. but a new question, why I can't got the result as your picture?

SMath have two "=": Numerical and Symbolical. With numerical evaluation you can only obtain numerical values, that is, without undefined variables. Rigth click to change it to symbolic equals, or use Ctrl+period instead "=", or click symbolic evaluation in the right panel.

Wrote

would you mind post the sample sm file ?

Sorry, I forgot to post it, and right now can't.

Best regards.
Alvaro.

thank you!

I got it.

Thanks a lot!
John

OBSERVE ... so much from so little

Solve Algebraic, NON-Algebraic Read first.sm (69,81 KiB) scaricato 1274 volta(e).

This multi solve companion is 3 x 3
Make it 2 x 2 ... n x n ... as per your project.

Solve Algebraic, MULTISOLVE Companions.sm (17,86 KiB) scaricato 1301 volta(e).

You can automate assigning guesses to unknowns.
By this way, you won't care order of them.

Regards

findroot_auto.sm (4,48 KiB) scaricato 1216 volta(e).

Wrote

For your example, make it algo style for local infinite use.
Observe ... sols:=U^-1*V is universal outside of Smath Plugin(s)

... your question about order of vars
solutions are by convention in descending order of the pair wise u, v
no matter the names you give.
I can't explain the decimals difference between MCD 11/Smath.
There are other constants that can't be found exactly ...
Pitot constant, Goat radius constant ...
That remark applies to any solvers [Smath and wrt any CAS]
The U^1*V is the core component of the Cholesky solver
as applied to fitting model function to a data set.
In that case, best fit is obtained by iterating the Genfit.
Chers ... Jean.

... here, you can push the cork in the bottle to accommodate irrational pi.
as well ignore epsilon.

... as it looks, the max I could push the cork in the bottle
y≡0.279339266990994 ... sanity f(x,y,z)=-0.000000000001344
Confirms impossible exactly solving irrational numbers.

Long word short, there is an order for vars.
You can either avoid it manually or automatically.
It is up to users choice which suits them most.
Either one has advantages over other.

Regards

Thank you all so much!

a nice forum

I never thought the time would come when I would become an expert at ignoring specific comments on a forum...thanks Jean!

Wrote

Thank you all so much !

Solving is very important in Engineering Projects.
Reserve ... solve, roots, FindRoots and more to specific applications
Solving a square matrix goes via the conventional solver, no flaw.
This didactic document has been refreshed.
Cheers ... Jean.

Solve Algebraic, MULTISOLVE DIDACTIC.sm (21,05 KiB) scaricato 1295 volta(e).

Wrote

I never thought the time would come when I would become an expert at ignoring specific comments on a forum.
...Thanks Jean!

Many of the advanced Smath documents are join venture.
Adapted/exemplified from various sources.
Download: Samples, Utilities Most used_3.
If something is not clear, please don't hesitate.
You have more, please offer.
Take care Amigo ... Jean.

No churichruo, dont.
If you will post same worksheets 600 times, (satire here)
and then you will tease how less another one contributed,
and how your post statistic is 18.3% of entire forum,
Please don't.

You will just make a fool of yourself.

Wrote

No churichruo, dont.
...
You will just make a fool of yourself.

Do you mean churichruo will make a fool of himself
from reputed contributors in this document:
Mathsoft, Robert Adair, Carlos, Martin, Viacheslav, Romberg,
Riemann FD, Hermite Polyline, Legendre, Gram_Schmidt,
Guiseppe Borzi [simplex], Mathsoft Collaboratory Convolution ...
I will add Fresnel [Clothoid].
churichruo wrote Tanks Jean