ENG 4350/5340: Project 2
Assigned: June 9,2015
Due: June 23, 2015
• 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
Consider the function f(t) = −t 3 + 2t 2 + t + 2 on the closed interval t ∈ [−2, 2].
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
3. Solve the normal equations using the SVD and calculate the error, E. Write your approximated function,
4. Plot f(t), fˆ1(t) and fˆ2(t) on the same plot.
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.