Engineering Asignment

ENG 4350/5340: Project 2

Assigned: June 9,2015

Due: June 23, 2015

Rules

Use C or C++ with BLAS/LAPACK for completion of this assignment.

Produce a LATEX-generated PDF of your report.

Ask plenty of questions to ensure you have a good understanding of the project.

The code (and reports) should look vastly different for different groups. Very similar code will incur a

hefty penalty.

Consider the function f(t) = t 3 + 2t 2 + t + 2 on the closed interval t [2, 2].

Part 1

1. Sample f(t) to produce f(t k) where k [1, 10] ⊂ Z. The t k should be randomly chosen points on the

interval [2, 2]. Produce a table with columns t k and f(t k). Ensure that the t ks are not sorted.

2. Solve the normal equations using QR decomposition and calculate the error, E. Write your approximated

function, fˆ1(t).

3. Solve the normal equations using the SVD and calculate the error, E. Write your approximated function,

ˆf2(t).

4. Plot f(t), fˆ1(t) and fˆ2(t) on the same plot.

Part 2

In this part we will see how additive random noise affects our solution.

1. Create a new dataset by doing the following:

Sample f(t) to produce f(t k) where k [1, 1000] ⊂ Z. The t k should be randomly chosen points

on the interval [2, 2]. Use a different random seed than used in the previous part.

Add columns y 1(t k) = f(t k) + n 1(t k) and y 2(t k) = f(t k) + n 2(t k) where n 1(t) ∼ N(0, 1) and

n 2(t) ∼ N(0, 5) to the dataset.

2. Solve the normal equations for this new dataset. NOTE: This dataset should be solved simultaneously

with 3 right hand sides.

3. Include the error in your report.