Improving Calculation Accuracy - Determining the zeros of an equation using "solve" function and using Newton's method - Сообщения
Found an error in the last question. I am attaching the updated file.
Improving Calculation Accuracy.sm
Improving Calculation Accuracy.sm
Improving Calculation Accuracy.pdf
Best regards.
Alvaro.
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
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
...
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
Equation with Bessel functions.pdf
Best regards.
Alvaro
1. rootDichotomy for the roots.
2. rootSecant for solving intersection with linear f(x) ... typical.
Jean.
Bessel SOLVE.sm
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?
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
Equation with Bessel functions Explain.pdf
Best regards.
Alvaro.
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.
Hi. Some comments added.
Best regards.
Alvaro.
Mentioned procedure for finding when solve(), diff(), etc would work is useful.
Thanks
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.
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
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
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
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
... 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 ... !
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
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
It was extremely important to get feedback on this issue.
Now my knowledge of mathematics and programming has been improved.
Best regards,
Nikolai
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
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