Summer I 2021 MATH 110A Midterm II Due at 12PM on Jul 28, 2021
Perform all of the following in a single Matlab file. Name this file MidtermII YourName.m. All commands
should be followed by a semi-colon “;” so that when the script is run, nothing middle step gets displayed
to the screen.
In order to measure the tool wear rate, we do this experiment: after time t (e.g., every an hour), we
measure the thickness of the tool and get the data as below:
order number n 0 1 2 3 4 5 6 7
time tn (h) 0 1 2 3 4 5 6 7
thickness yn (mm) 27.2 26.9 26.6 26.3 26.1 25.8 25.3 24.3
Find the relation y = f(t) between y and t.
1. (10 points) Plot the points (tn, yn), n = 0, · · · , 7. Label t-axis and y-axis. Title “Your Name”.
2. (20 points) Use the least square method to find y = f(t) = at+ b, where a and b are constants.
3. (20 points) Use the recursive least square method to find y = f(t) = ant + bn, n = 0, · · · , 7, where
an and bn are constants.
4. (10 points)
Plot y = f(t) = at + b from 2. Use red color. Legend “least square method” on this plot.
Plot y = f(t) = ant+bn from 3. Use blue color. Legend “recursive least square method” on this plot.
5. (20 points) Use “Minimum Norm” to find the point (t, y) on y = f(t) such that the distance to
(0, 0) is shortest. t rounded to nearest 4-th. Label this point on the above plot.
6. (20 points) Use “Kaczmarz’s Algorithm” to find the point (t, y) on y = f(t) such that the distance
to (0, 0) is shortest. The results are displayed in the Command Window in the following format: “There
are N iterations to get the point (t, y).” where N is the stage that t rounded to nearest 4-th.
Make sure you only have one plot display in your project.























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