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Approximate a smooth f(x,y) function with a polynomial function
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approximatepolynomialwithfunctionsmooth
Problem
I have a discrete function of two real variables defined as a set of point in a rectangular domain. The function is smooth. I need to approximate it with a polynomial function of the 2nd degree with the error as little as possible. What algorithm can I use to find out the constants for the polynomial?
Solution
Wikipedia:
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable $x$ and the dependent variable $y$ is modelled as an $n^{th}$ degree polynomial in $x$.
One possible solution is the polynomial regression, that is, curve fitting method. Given a set of points $Y$ you may use one of two algorithms: closed form solution or gradient descent. When number of points is very large then the gradient descent is faster than closed form solution. Also note that we measure error using residual sum of squares (RSS). Both algorithms finds coefficients by minimizing the RSS. This post may help as well.
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable $x$ and the dependent variable $y$ is modelled as an $n^{th}$ degree polynomial in $x$.
One possible solution is the polynomial regression, that is, curve fitting method. Given a set of points $Y$ you may use one of two algorithms: closed form solution or gradient descent. When number of points is very large then the gradient descent is faster than closed form solution. Also note that we measure error using residual sum of squares (RSS). Both algorithms finds coefficients by minimizing the RSS. This post may help as well.
Context
StackExchange Computer Science Q#77863, answer score: 3
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