Surface Fitting Different Algorithms

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?

[John D'Errico]

This is WAY to large of a question to answer in less than a book. In fact, you could find dozens of books on the concepts involved.

[Mohan Gopal Tripathi]

Thanks for replying.

Yes, indeed its a question for not less than a book. I am using it for a surface fitting and i have nothing to do with mathematics. But i must know that what i am using to find the fit surface. So i am looking for a summary which tells me some basic answers. Like the algorithm used. I have created the surface using all methods with different models, but i cant tell exactly what algorithm or maths i am using for each method.

I hope you are understanding my confusion.

[John D'Errico]

So what are we supposed to say? Write the book that you need to read?

Do some reading, perhaps on Wikipedia. Do you really need to know the algorithms behind a fit? If you want that, then read the docs for the tools in question. They will usually show a reference. Perhaps what you need to take is a course on empirical modeling. Lacking that, READ A BOOK. This question (and your several related questions) is far to extensive to answer here, as it would require writing a book.

[Mohan Gopal Tripathi]

Thanks for replying.

There is no need to be rude and insulting by saying "Write the book you need to read". I know the value of time and the much of time you invested in answering my queries. Thanks again.

With all due respect if you dont feel like answer DONT ANSWER. No need of being rude and insulting.

If you know more than me in MatLab, does not give you right to insult by answering like this.

I have read the documentation of the MatLab and i have not found the satisfactory answer. I just want to get the upper layer of the methods not in deep. I am testing some sensors and need the data to be presentative, so i used MatLab, but also i need to know and explain why i used particular method, which helps me defending my research properly.

Anyways , Thankyou very much. I will figure it out by Myself. Thanks again.

[Image Analyst]

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.