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Offline Neeky  
#1 Posted : 24 August 2022 17:25:23(UTC)
Neeky

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Dear forum users! I turn to you for advice on the SMath program. I am attaching a file in .sm format with suggestions for improving the accuracy of calculations in the SMath program and questions for the presented calculation.

Found an error in the last question. I am attaching the updated file.

Improving Calculation Accuracy.sm (79kb) downloaded 9 time(s).

Edited by user 26 August 2022 10:29:46(UTC)  | Reason: Error in the last question

Offline Razonar  
#2 Posted : 25 August 2022 01:15:42(UTC)
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Hi Neeky. Some notes about your questions.

Improving Calculation Accuracy.sm (34kb) downloaded 20 time(s).
Improving Calculation Accuracy.pdf (255kb) downloaded 27 time(s).

Best regards.
Alvaro.
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on 25/08/2022(UTC),  on 25/08/2022(UTC)
Offline Jean Giraud  
#3 Posted : 25 August 2022 13:59:00(UTC)
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... this version for your convenience.
Previous deleted.

Improving Calculation Accuracy RootSecant.sm (29kb) downloaded 16 time(s).
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on 25/08/2022(UTC)
Offline Neeky  
#4 Posted : 26 August 2022 16:36:02(UTC)
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Thank you very much for the tip to use the bisection method!

Please tell me how it is possible to implement in the SMath program an algorithm for calculating the roots of an equation that (an equation) contains Bessel functions. Equation with Bessel functions.sm (4kb) downloaded 8 time(s).
Offline Jean Giraud  
#5 Posted : 26 August 2022 20:24:54(UTC)
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Originally Posted by: Neeky Go to Quoted Post
Please tell me how it is possible to implement in the SMath program an algorithm for calculating the roots of an equation that (an equation) contains Bessel functions

Immediately, answer is no from Smath built-in Bessel... Why ?
Smath built-in Bessel has no derivative for roots solver.
Visit ► Samples ► Solve Grand TREASURY ► sheet 0
You can have Bessel from Computer Approximation ... attached.
Cheers ... Jean.

Bessel J0,Y0.sm (23kb) downloaded 10 time(s).
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on 29/08/2022(UTC)
Offline Razonar  
#6 Posted : 27 August 2022 04:25:12(UTC)
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Originally Posted by: Neeky Go to Quoted Post
...
Please tell me how it is possible to implement in the SMath program an algorithm for calculating the roots of an equation that (an equation) contains Bessel functions.


Hi. Use bisection method.

Equation with Bessel functions.sm (25kb) downloaded 20 time(s).
Equation with Bessel functions.pdf (78kb) downloaded 12 time(s).

Best regards.
Alvaro

Edited by user 27 August 2022 04:28:52(UTC)  | Reason: Not specified

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on 29/08/2022(UTC)
Offline Jean Giraud  
#7 Posted : 27 August 2022 15:20:06(UTC)
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This document solve Smath built-in mwbesselj(0,x)
1. rootDichotomy for the roots.
2. rootSecant for solving intersection with linear f(x) ... typical.
Jean.

Bessel SOLVE.sm (23kb) downloaded 13 time(s).
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on 29/08/2022(UTC)
Offline Neeky  
#8 Posted : 29 August 2022 15:47:41(UTC)
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Thanks for the help.
Now I can determine the roots of such equations.
My calculations that contain these equations are calculated correctly.
The only thing I don't understand is the algorithm presented in Razonar's post..
Could you please tell me how to deal with this algorithm?
Offline Razonar  
#9 Posted : 29 August 2022 21:23:42(UTC)
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Originally Posted by: Neeky Go to Quoted Post
Thanks for the help.
Now I can determine the roots of such equations.
My calculations that contain these equations are calculated correctly.
The only thing I don't understand is the algorithm presented in Razonar's post..
Could you please tell me how to deal with this algorithm?


Hi. Some comments added.

Equation with Bessel functions Explain.sm (43kb) downloaded 10 time(s).
Equation with Bessel functions Explain.pdf (259kb) downloaded 8 time(s).

Best regards.
Alvaro.

Edited by user 29 August 2022 21:30:15(UTC)  | Reason: Not specified

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on 30/08/2022(UTC),  on 30/08/2022(UTC)
Offline Jean Giraud  
#10 Posted : 29 August 2022 22:47:10(UTC)
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Originally Posted by: Neeky Go to Quoted Post
Now I can determine the roots of such equations.

If you provide a sample, that will help mutually.
As offered, you can solve for roots & intersections.

Offline overlord  
#11 Posted : 30 August 2022 00:07:27(UTC)
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Originally Posted by: Razonar Go to Quoted Post
Hi. Some comments added.

Best regards.
Alvaro.

Mentioned procedure for finding when solve(), diff(), etc would work is useful.

Thanks

2022-08-30_00-05.png
Offline Neeky  
#12 Posted : 30 August 2022 11:14:28(UTC)
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Hello!

Thank you very much for your clarification and for taking the time to answer my question.

Due to the fact that I am not a mathematician or a programmer, it is still very difficult for me to understand these algorithms.

Best regards.
Nikolai.
Offline Jean Giraud  
#13 Posted : 30 August 2022 17:43:23(UTC)
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Originally Posted by: Neeky Go to Quoted Post
Due to the fact that I am not a mathematician or a programmer, it is still very difficult for me to understand these algorithms.
Best regards.
Nikolai.

You have to be the Smth Mathematician in some of these built-in functions.

BesselJ(x,0)... is strctly 0 from x=0 ... ∞
Thus, you can multiply by anything.
As a desirable effect, it constrains
x*BesselJ(x,1)to start @ 0
for profitable inspection suite.
Psi(x)+BesselJ(x,0)renders superbly Psi(x).
What complains here is for smarter than me
Cheers ... Jean.

Neeky.sm (22kb) downloaded 6 time(s).


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Offline Jean Giraud  
#14 Posted : 01 September 2022 01:01:45(UTC)
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Hello Nikolai,
Your Bessel PDF is interesting.
It has a close relationship with Weibull.
As demonstrated, not optimized.
Added solve roots/datum, accurate algo style.
Cheers ... Jean.

Stat Treasury_11 PDF Weibull_Bessel.sm (17kb) downloaded 5 time(s).
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on 01/09/2022(UTC)
Offline Neeky  
#15 Posted : 01 September 2022 17:23:46(UTC)
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Originally Posted by: Jean Giraud Go to Quoted Post
Hello Nikolai,
Your Bessel PDF is interesting.
It has a close relationship with Weibull.
As demonstrated, not optimized.
Added solve roots/datum, accurate algo style.
Cheers ... Jean.

Stat Treasury_11 PDF Weibull_Bessel.sm (17kb) downloaded 5 time(s).


Hello Jean Giraud,

Thank you for your attention to my questions and for tips on how to improve the accuracy of calculations.

The equation whose roots I need to find is correctly written in SMath:
F(x) = x * Bessel(1;x) - 1,01 * Bessel(0;x).

Tell me, please, is it possible to apply the algorithm you proposed to determine the roots of this equation?

Best regards,
Nikolai
Offline Jean Giraud  
#16 Posted : 01 September 2022 19:55:17(UTC)
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Originally Posted by: Neeky Go to Quoted Post
... is it possible to apply the algorithm you proposed to determine the roots of this equation?

Immediate answer is NO from brute force.
I try to manage my Waterloo ... !
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on 02/09/2022(UTC)
Offline Jean Giraud  
#17 Posted : 01 September 2022 23:36:35(UTC)
Jean Giraud

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Originally Posted by: Neeky Go to Quoted Post
Tell me, please, is it possible to apply the algorithm you proposed to determine the roots of this equation?

Now, answer is YES from individual Dichotomy.
Accuracy is in the range of ~ 15 D.
Enjoy ... Jean.

Nikolai roots.sm (45kb) downloaded 9 time(s).
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on 02/09/2022(UTC)
Offline Jean Giraud  
#18 Posted : 02 September 2022 14:37:58(UTC)
Jean Giraud

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Originally Posted by: Neeky Go to Quoted Post
The equation whose roots I need to find is correctly written in SMath:
F(x) = x * Bessel(1;x) - 1,01 * Bessel(0;x).
Tell me, please, is it possible to apply the algorithm you proposed to determine the roots of this equation?

... here is your project Nikolai !
As far as I understand your roots demand.
f(x) is not scalar wrt 'x' for the solver/scanner solve(■,■,■,■)
but compatible with roots-Dichotomy command line.
Please, don't hesitate for more ... Jean.

Nikolai roots.sm (59kb) downloaded 9 time(s).
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on 02/09/2022(UTC)
Offline Neeky  
#19 Posted : 02 September 2022 15:35:52(UTC)
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Jean and Alvaro thank you very much for your efforts.

It was extremely important to get feedback on this issue.

Now my knowledge of mathematics and programming has been improved.

Best regards,
Nikolai
Offline Jean Giraud  
#20 Posted : 02 September 2022 21:50:21(UTC)
Jean Giraud

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Originally Posted by: Neeky Go to Quoted Post
Jean and Alvaro thank you very much for your efforts.

This augmented version includes min/max Golden ratio.
In case you would want to fit upper/lower envelope,
you will need those support points and more.
Cheers ... Jean.

Nikolai roots.sm (79kb) downloaded 6 time(s).
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