Purpose

The purpose of this lab assignment is to use the Matrix class from lab 2 to explore least squares polynomial curve fitting.

Assignment

In this lab, you are to do the following:

• Design and implement a method for obtaining the best fit (in the least squares sense) polynomial curve to a set of data.
• You should reuse the Matrix class where appropriate.
• Input should be accepted from a data file with the following format:

    5
    300 0.024
    400 0.035
    500 0.046
    600 0.058
    700 0.067
    

  where the first line indicates the number of x,y pairs and each additional line specifies an x,y pair.
• The program should output (to the console or to a file) the equations for the first, second, and third order polynomials fit to the input data and the corresponding variance.
• Generate a couple of data sets to test your program.
• Use your program to answer the following question (similar to textbook question 3.89): Experimental data for the emittance of tungsten as a function of temperature has been report to be:

        T (Kelvin) |   300   400   500   600   700   800
        -----------+------------------------------------
        Emittance  | 0.024 0.035 0.046 0.058 0.067 0.083
  
        T (Kelvin) |   900  1000  1100  1200  1300  1400
        -----------+------------------------------------
        Emittance  | 0.097 0.111 0.125 0.140 0.155 0.170
  
        T (Kelvin) |  1500  1600  1700  1800  1900  2000
        -----------+------------------------------------
        Emittance  | 0.186 0.202 0.219 0.235 0.252 0.269
        

  The researchers claim that the following equation accurately represents the emittance for all temperatures (to three decimal places):

        e(T) = 0.02424*pow((T/303.16),1.27591)
        

  Suppose that we wish to find the emmitance of tungsten at 350, 450, 550, ... , 1850, and 1950 K. What degree polynomial is required to match to the equation proposed by the researchers? Discuss the advantages and disadvantages interpolating instead of using their equation.

For this project, you are to work individually.

Lab report (due 4:30pm Tuesday, October 12, 1999)

This week, your lab report need not be self-contained. Your report should include:

• Discussion containing:
  • A brief description of any problems you encountered and how they were resolved
  • A brief description of your test plan
  • A brief description of your approach for answering the questions (along with your answers)
  • Any questions you have regarding the lab
  • Suggestions for how the lab could be improved in the future
• Documented source code
• The data files that you created as well as their corresponding output

As with any report you submit, correct spelling and grammar are required. In addition, your report should be submitted electronically following the Electronic Submission Guidelines. (You may wish to consult the sample report before submitting your report.) Be sure to keep copies of all your files, in case something gets lost. It may be wise to keep a diskette backup as well.

If you have any questions, consult the instructor.

This page was created by Dr. Christopher C. Taylor, copyright 1999.