3rd degree fit, given 5 data points (math is needed for client)

[kepler]

Hi,

I need to know how the formula of the coeficients of a third degree polynomial best fit to 5 points (x1,y1,x2,y2,x3,y3,x4,y4,x5,y5). Since it's for a pressing project for one of my clients, I remembered to ask for help here. I really don't have the time to calculate the matrice for the linear system, etc.

Can someone help? I would apreciate.

Kind regards

Kepler

 

[tkhunny]

Hi,

I need to know how the formula of the coeficients of a third degree polynomial best fit to 5 points (x1,y1,x2,y2,x3,y3,x4,y4,x5,y5). Since it's for a pressing project for one of my clients, I remembered to ask for help here. I really don't have the time to calculate the matrice for the linear system, etc.

Can someone help? I would apreciate.

Kind regards

Kepler

3rd degree polynomial has four parameters. Matching 5 points requires 4th degree to guarantee collocation. You might get lucky, I suppose.

 

[Dr.Peterson]

I need to know how the formula of the coeficients of a third degree polynomial best fit to 5 points (x1,y1,x2,y2,x3,y3,x4,y4,x5,y5). Since it's for a pressing project for one of my clients, I remembered to ask for help here. I really don't have the time to calculate the matrice for the linear system, etc.

I'm not quite sure what you are asking for. You are looking for the best fit of a cubic polynomial to 5 given points (not for an exact fit); presumably you have some reason to want a cubic specifically. You clearly know something about the relationship to matrices; you ask for a "formula", but evidently you mean something more than the formula (in terms of matrices) found, say, here.

Do you need to write a program to do this for the client, or are you looking for appropriate software, or do you want us to carry out the process for you for a specific set of points, or what? If you have specific numbers, you could just fit the curve using Excel or other readily available tools. But I don't think you could turn the whole regression process into a simple formula if you just mean an explicit expression in your ten variables. It would probably be very ugly. That's why it is expressed using matrices. What is it that you don't have time to do?

 

[kepler]

I'm not quite sure what you are asking for. You are looking for the best fit of a cubic polynomial to 5 given points (not for an exact fit); presumably you have some reason to want a cubic specifically. You clearly know something about the relationship to matrices; you ask for a "formula", but evidently you mean something more than the formula (in terms of matrices) found, say, here.

Do you need to write a program to do this for the client, or are you looking for appropriate software, or do you want us to carry out the process for you for a specific set of points, or what? If you have specific numbers, you could just fit the curve using Excel or other readily available tools. But I don't think you could turn the whole regression process into a simple formula if you just mean an explicit expression in your ten variables. It would probably be very ugly. That's why it is expressed using matrices. What is it that you don't have time to do?

Good evening,

Yes, I was asking for help in the determination (formulation) of the best cubic polynomial fit coeficients for 5 set of points. And no: no program will be writen. If I had the general form of each coeficient, I would then replace with the job asked arguments (also linear formulas). The project is a thesis - thus the the need of numeric answers, and not "loop" routines, or general presentation of matrices.

Either way, I solved the problem by calculation the determinants, using Kramer rule, and simplified after that.

But thanks anyway

Kind regards,

Kepler

 

[Dr.Peterson]

Yes, I was asking for help in the determination (formulation) of the best cubic polynomial fit coeficients for 5 set of points. And no: no program will be writen. If I had the general form of each coeficient, I would then replace with the job asked arguments (also linear formulas). The project is a thesis - thus the the need of numeric answers, and not "loop" routines, or general presentation of matrices.

Either way, I solved the problem by calculation the determinants, using Kramer rule, and simplified after that.

In other words, what you wanted was just a way to do this for some particular numbers, and you found one, so nothing more is needed. Good.

If you did need more, you might give an example of the numbers you have, so we could suggest particular ways (and see if our different methods agreed).

 

[kepler]

In other words, what you wanted was just a way to do this for some particular numbers, and you found one, so nothing more is needed. Good.

If you did need more, you might give an example of the numbers you have, so we could suggest particular ways (and see if our different methods agreed).

Thank you very much for your kindness and help

Kind regards

Kepler