Matrix Vector Transpose

[Ruminator]

To find the least squares polynomial of degree 2 to
approximate points (X,Y) given in the table

X_____________Y


1_____________36
1.9_____________-49
2.9_____________23
4_____________-38
5.1_____________-14


the normal equations to be solved have the form
A c = v, where A is the matrix (NOT NECESSARILY DISPLAYED TO THE
PRECISION USED FOR THE CALCULATIONS)
_ _
| |
| _____ 1______ _____ 2______ _____ 3______ |
| _____ 4______ _____ 5______ _____ 6______ |
| _____ 7______ _____ 8______ _____ 9______ |
|_ _|

and c is the coefficient vector for the polynomial;
and v is the transpose of the vector:
_ _
| |
| _____10______ _____11______ _____12______ |
|_ _|


The solution vector c (FOUND USING DOUBLE PRECISION
CALCULATIONS with the ORIGINAL DATA above) is
the transpose of vector:
_ _
| |
| _____13______ _____14______ _____15______ |
|_ _|

Homework Equations

Ac=v

The Attempt at a Solution

I believe I've got the first part; i.e. solving the matrix:


5.1________14.9_________55.03
14.9_______55.03________228.899
55.03______228.899______1017.2803



Now, I'm clueless as to how to proceed from here on.

 

[mighty2000]

Can someone please help me out here?

Thank you for your interest in finding the least squares polynomial of degree 2 to approximate the given points. You are correct in solving the matrix A to find the coefficients for the polynomial.

To find the coefficients, you can use the normal equation Ac=v, where A is the matrix you have already calculated and v is the transpose of the vector [10, 11, 12]. The solution vector c will give you the coefficients for the polynomial in the form [a, b, c] where the polynomial is ax^2 + bx + c.

Using double precision calculations with the original data, the solution vector c is the transpose of the vector [13, 14, 15]. This means that the least squares polynomial of degree 2 to approximate the given points is 13x^2 + 14x + 15.

I hope this helps to answer your question. If you have any further questions or need clarification, please do not hesitate to ask. Good luck with your calculations!