Hi Nawras, what is the goal exactly ? Do you want to find z as a function of x and y or a general equation of the form f(x,y,z)=0 ?

Hi Epenoy,

z as a function of x and y, that is z is dependent variable and both of x and y are independent variables.

Tq.

Hi, you can first plot the discrete values you have and then decide for the best model to fit the data (linear, quadratic, .. The difficulty is that you have few data and the model will certainly do not match very well.

Hi, this fits in the problem of bivariate interpolation, a classical matter in numerical analysis. You can get z as a polynomial in x and y. You can also get best approximating functions (linear, Bezier, etc). There are programs that can compute it.

Hi Mickael,

Thanks a lot. Can you suggest some  programs that able to compute the formula directly from given data?

Tq.

No sorry, I'm not an expert in numerical matters. You may find useful references in such kind of survey : http://link.springer.com/article/10.1023/A:1018981505752

Good luck.

Dear Dr. Nawras,

Please check this link:

www.mathworks.com/matlabcentral/answers/98925-is-it-possible-to-fit-data-to-more-than-two-independent-variables-using-curve-fitting-toolbox-r2013b

Best regards,

Muhammad

Dear Dr. Nawras

you can use spss to get you the equation for 3 independent variables with its R-squared Regression

Thank you Mr. Muhammad Abdulrasool and Mr Ahmed Sh. Yasiry for your valuable sharing. I will try using SPSS hoping it can do the job. 

Regards,

Also OriginPro, is a giod choice. 

It can fit 3 variables of a surface plot, may be it's what you want

It is working with SPSS

Analyze>regression>linear

 However, for nonlinear order it is very difficult to perform as it needs a professional user in statistical analysis.

Thanks a lot for every one who shared his knowledge 

The answer is no. There is a simple example: f(x) = 1/(x+1) sin x^2. The function vanishes at infinity but the derivative not. 

Best regards 

Joerg

Try SPSS, I have used it on polynomials

y = 50.9847530867483 + 1.96275171976368*x + 0.02473449895648*z^4 + 0.0526317346135648*z*x^2 + 3.66209051246064*tanh(x*sin(z*sinh(x*z))) - x*z

Using Eureqa Formulize.

without sin, sinh and tanh

y = 22.1343029549693 + 10.8292764965611*x + 0.296189687976693*x*z^2 + 27*z/x^2 - 2.11016161227361*x*z - 0.270179597887278*x^2

To Mohd Akmal Masud

given by Muhammad Abdulrasool ?