Handy Polynomial Fitting with Bernstein Polynomials

[Namir]

Thomas,

I was doing a regression with Bernstein basis polynomials terms. I do not use the term f(j/n). With orders of 4 or 5 I get good results.

In my Excel sheet column A has the original values of x, and column B has the normalized values of x. Column C has the y data. To calculate the fits row of Bernstein basis polynomials terms based on the x(1) value in cell B2, I use the following formulas:

=COMBIN(4,0)*(1-B2)^4 in cell E2
=COMBIN(4,1)*B2*(1-B2)^3 in cell F2
=COMBIN(4,2)*B2^2*(1-B2)^2 in cell G2
=COMBIN(4,3)*B2^3*(1-B2) in cell H2
=COMBIN(4,4)*B2^4 in cell I2

I then replicate these formulas down the rows of data and then use Excel Analysis Tool to perform multiple regression. I specified that the model include a constant term. This choice is optional.

Namir