Handy Polynomial Fitting with Bernstein Polynomials
11-11-2018, 01:51 PM (This post was last modified: 11-11-2018 02:56 PM by Namir.)
Post: #6
 Namir Senior Member Posts: 823 Joined: Dec 2013
RE: Handy Polynomial Fitting with Bernstein Polynomials
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
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 Messages In This Thread Handy Polynomial Fitting with Bernstein Polynomials - Namir - 11-10-2018, 10:22 PM RE: Handy Polynomial Fitting with Bernstein Polynomials - Valentin Albillo - 11-11-2018, 03:10 AM RE: Handy Polynomial Fitting with Bernstein Polynomials - Namir - 11-11-2018, 06:00 AM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Klemm - 11-11-2018, 05:12 AM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Klemm - 11-11-2018, 01:39 PM RE: Handy Polynomial Fitting with Bernstein Polynomials - Namir - 11-11-2018 01:51 PM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Klemm - 11-12-2018, 05:39 AM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Okken - 11-12-2018, 01:21 PM RE: Handy Polynomial Fitting with Bernstein Polynomials - Thomas Klemm - 11-12-2018, 02:09 PM

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