 CS-381 -- Lab 3: Least Squares Interpolation

Fall Quarter 1999

Electrical Engineering and Computer Science Department
Dr. Christopher C. Taylor

S-331, 277-7339 www.msoe.edu/~taylor/

### 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