Polynome regression
Abstract
Fitting of polynomes to a given set of data is one of the most common methodes of regression. Simple problems can easly be solved by use of standard programs. Though, if userdefined polynomes are required, the algorithms have to be hard-coded since the system of equations become complex quite fast. The case is even more demanding, if the polynome is multi dimensional.
In this framework exponent matrices are applied which are built up systematically and represent the structure of the system of equations. Once these matrices are built as many datapoints as demanded can be included.
The proposed algorithm solves two problems at the same time: First the desired polynome can easily be prompted in the shape of a potence matrix and can therefore be adjusted within seconds. Second, the dependence of multiple variables (multi dimensional) is handled with ease and it's fast (1.45 seconds for 55'696 datapoints in 2 dimensions with 15 coefficients in Scilab).
In this framework exponent matrices are applied which are built up systematically and represent the structure of the system of equations. Once these matrices are built as many datapoints as demanded can be included.
The proposed algorithm solves two problems at the same time: First the desired polynome can easily be prompted in the shape of a potence matrix and can therefore be adjusted within seconds. Second, the dependence of multiple variables (multi dimensional) is handled with ease and it's fast (1.45 seconds for 55'696 datapoints in 2 dimensions with 15 coefficients in Scilab).