Surface Fitting Different Algorithms

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I am recently working with the Surface Fitting. I came across three methods to do it, which are Regression, polynomial, interpolation and smoothing. I want to know about the algorithm used in each method. I dont understand the concept of Least Square Method. Is this is used in all surface fitting methods? Is there any documentation stating the algorithm used by each methods. How all the different surface fitting works and what is the maths behind it?
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Image Analyst
Image Analyst 2019-5-24
Give an example of the data you want to fit a surface to, like a .mat file, or a screenshot, or both. Do you want the result to be a 2-D matrix with z values for every grid point? Do you want the fitted surface to match the existing training points (like a regression rather than a spline interpolation)?
Mohan Gopal Tripathi
Thanks for replying.
I already have fitted the surface. I want to estimate the unknown variable with the help of two other variables. I have data for all 3 variables and from those i want to estimate. I sucessfully plotted it , estimated it with the accuracy of 90%. All is Done. I used Interpolation as it is the best fit with less error. I used all four which i mentioned above.
Now i want to defend my research, so i want to know how they work. Is there any algorithm behind it? Or some thing which differntiate different methods. Else i will look into the code of the fit function and understand by myself.
Please dont invest your much time in it, because i may keep asking questions.I already had a insulting experience before.

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