hwkHouseholder

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Due Date

See the calendar for due date.

Description:

For n = {0,1, ..., 5}, fit a polynomial of degree n by least squares (using Householder QR Factorization) to the following data:

t	y
0	1.3
1	3.4
2	6.3
3	7.1
4	8.8
5	9.2

Read in the data from a file and make a plot (e.g., using gnuplot) of the original data points with each resulting polynomial curve. Which polynomial best captures the general trend of the data? Why?

Assignment

1. Write a solution to the problem using pseudocode
2. Write a Fortran program with a subroutine that performs Householder QR Factorization and calculates the coefficients of the polynomials
3. Extend the Fortran program with another subroutine that utilizes a LAPACK Householder routine that calculates the coefficients of the polynomials
4. Name your variables the same name as the ones used in the textbook
5. Write a report (typeset with LaTeX) that:
   1. Explains what you learned completing this exam
   2. Describes the process that you went through to come up with the algorithm and the solution
   3. Reports the polynomials, which one best captures the data and why
   4. Includes what you did to verify that you obtained the right / good approximation to the problem
   5. Includes how long it took you to complete this midterm
6. Submit the report as a PDF.

Feel free to utilize a Matlab / Octave prototype of your approach.

Rubric:

Points       Item
-----------  --------------------------------------------------------------
_____ / 10   Pseudocode
_____ / 55   Fortran Householder subroutine (with comments)
_____ / 10   Fortran LAPACK Householder subroutine (with comments)
_____ /  7   Project writeup (overall)
_____ /  9   Project writeup: Algorithm and solution process
_____ /  9   Project writeup: Verification approach

_____ /100   Total

_____  Approximate number of hours spent
      

Submission

Place the following in a tarball and submit the tarball into the appropriate folder in the dropbox for COMS 6100 at https://elearn.mtsu.edu:

1. Pseudocode
2. A makefile that will compile your code correctly
3. Fortran source code
4. Report (as a PDF)
5. Completed rubric (estimates for each line including hours spent)

To make a tarball, do something like the following:

tar -czf hwkHouseholder.tar.gz  hwkHouseholder/

Suggestions

• Make progressive progress by printing out intermediate values and checking them against
  1. Example 3.8 in the textbook (hard code the values from Example 3.1)
  2. Your prototype solution
• Start with just one value of n, then move to other values
• If your having troubles reading in data from a file, take a break from that and hard code the values. (Don't forget to go back and read in the data from a file.)