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December 19th, 2016, 06:25 AM  #1 
Newbie Joined: Dec 2016 From: Belgrade, Serbia Posts: 1 Thanks: 0  Get equation that describes set of measures
Hello. A whole decade passed since I graduated mathematics and shifted to other profession, so my knowledge is very rusty. There is an important problem for a scientific work that I need help for. Let's say factor t is being calculated from factors x, y and z, all some parameters from living environment. There is a bunch of experimental measures where x, y and t were measured out precisely, but not z. z is a value that this work is about and is not measurable anyhow in reality. The question is how to determine a math equation that gives dependency between the 4 values : t = f(x,y,z) I understand standard interpolation requires known values for all variables in interpolation points, so I am not even sure the formulation of the problem is ok I do not know if it would be possible to do this even if z is known in all points, since this is a function from three variables. So my first question would be if it is possible to get this equation at all. If it is, I would be very glad that someone directs me to some interpolation method I could use to resolve this. I have tried with polynomial approximation: a_n*x^n + ... + a_1*x + a_0 + b_m*y^m + ... + b_1*y + b_0 + c_p*z^p + ... + c_1*z + c_0 = t When you substitute values from a very broad set of measured tests, this becomes a system of equations per following variables: a_n, ..., a_0, b_m, ..., b_0, c_p, ..., c_0, z where for z this goes to the power of p. This is obviously not solvable. So, there might be numerical analysis that could help, but I do not have knowledge to do this Thank you very much! 

Tags 
approximation, describes, equation, interpolation, measures, numerical analysis, set 
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