I want to find 4 constant with used 1 eq

Hello guy

How can I find 4 constant with used 1 equation?

My eq is ''ydata=x1*(1-exp(-x2*516))+x3*(exp(x4*516)-1)'' and I just have a ydata.

ydata=0.269

x1 x2 x3 x4 are my constant.

Thanks

Answer 1

[John D'Errico]

I'd like to solve a problem just like you. Let me pretend I have been given the equation:

a + b + c + d = 5

Can I determine all 4 variables? Is there any way I can learn the value of all 4 variables, given ONLY that one equation? So one data point only? The answer of course is no. At best you can pick the value of any three of those variables. Set them equal to any number you want. Then you can solve for the one variable you have not specified. That is the fundamental nature of an underdetermined problem - the one equation does not provide sufficient information.

If you have MULTIPLE data points, this becomes a different question. So if you have sufficient data points, then you can solve the problem. But you have said you have only one data point. (And I'm sorry, but the nice flowchart you have shown in a comment is not going to make the mathematics work.) An underdetermined problem is just that.

Answer 2

[Alan Weiss]

This is an underdetermined problem, meaning there are many different values of x1, x2, x3, and x4 that work. For example, choose any nonzero value for x2, and then you can solve for x1 given any values of x3 and x4:

Alan Weiss

MATLAB mathematical toolbox documentation

[Arash_ORD]

Hello Mr.Weiss.

Thanks for answer

Please If it's possible for you look the picture.

Thanks.

[Alan Weiss]

Is this a homework problem? If so, what have you tried? If not, then please describe the problem in your own words.

Alan Weiss

MATLAB mathematical toolbox documentation

[Torsten]

@Arash_ORD

It should be obvious that with one single value of t_exp (516) and one corresponding value for eps_exp (0.269), you will not be able to determine 4 senseful model parameters using "lsqnonlin". You will need many more - at least 4 values for t_exp and 4 corresponding values for eps_exp.

[Walter Roberson]

Suppose when you got to the test for being optimized, that you decided that they were not optimized. Your chart leads back to the lsqnonlin optiization. But that is a deterministic optimization, and the flow does not change any of the parameters, so you would get exactly the same result again, and would be stuck in an infinite loop.

[Arash_ORD]

Hello Mr. @Walter Roberson.

Thanks for answering my question.

[Arash_ORD]

Hello Mr. @Alan Weiss

Thanks for answering my question.

[Arash_ORD]

Hello Mr. @Torsten.

Thanks for answering my question.

[Arash_ORD]

Hello Mr. @John D'Errico.

Thanks for answering my question.