Instructions: In this take-home portion, we will be looking at the application of curve fitting. You
may work with each other on this but be sure you do the work. Must show all relative work to
receive credit. Part 1 has a total of 30 points which will be added to the in class portion of the
exam.
We wish to find a minimal polynomial that goes through the following points:
(-2,17),(1,2),(3,22)
The minimal polynomial to fit four data points would be a quadratic polynomial, that is a
polynomial in the form P(x)=ax^(2)+bx+c.
Do the following:
(3 points) Substitute in the order pairs into P(x) to find a linear system in terms of a,b,
and c.
Don't use any matrix yet in writing your system.
(You can see an example of this application in section 1.3 of our text)
(24 points) We will solve the system in 3 different ways (Note the result should be the
same).
a) Write the system as an Augmented matrix and apply Gaussian Elimination to solve
for the unknown coefficients.
b) Write the system in the form Ax=b. Find the inverse matrix of A and use it solve for
the coefficients.
c) Determine the LU-factorization of the matrix A. Use this factorization to solve for the
unknown coefficients.
(3 points) Note that your answers for 2), 3), and 4) should have given the same answer.
What is the quadratic polynomial that fits the given data points?
Instructions: In this take-home portion, we will be looking at the application of curve fitting. You
may work with each other on this but be sure you do the work. Must show all relative work to
receive credit. Part 1 has a total of 30 points which will be added to the in class portion of the
exam.
We wish to find a minimal polynomial that goes through the following points
(2,17), (1,2), (3,22)
The minimal polynomial to fit four data points would be a quadratic polynomial, that is a polynomial in the form P(x) = ax2 + bx + c.
Do the following:
1) (3 points) Substitute in the order pairs into P(x) to find a linear system in terms of a, b and c. Don't use any matrix yet in writing your system. (You can see an example of this application in section 1.3 of our text)
2) (24 points) We will solve the system in 3 different ways (Note the result should be the same). a) Write the system as an Augmented matrix and apply Gaussian Elimination to solve for the unknown coefficients.
b) Write the system in the form Ax = b. Find the inverse matrix of A and use it solve for
the coefficients.
c) Determine the LU-factorization of the matrix A. Use this factorization to solve for the unknown coefficients.
3) (3 points) Note that your answers for 2), 3), and 4) should have given the same answer. What is the quadratic polynomial that fits the given data points?
