Department of Computer Science
Sukkur IBA University
MS (CS/SE), Spring 2022
Subject: Advanced Computational Mathematics
Instructor: Dr. Fouzia Abdul Sattar
Max. Marks: 10
ASSIGNMENT # 3
Q.1. A missile is fired from enemy territory, and its position in flight is observed by
radar tracking devices at the following positions.
Position down range (miles)
0
250
500
750
1000
Height (miles)
0
8
15
19
20
Suppose our intelligence sources indicate that enemy missiles are programmed to follow
a parabolic flight path.
a) Plot the data points and the parabolic flight path using builtin Matlab command.
b) Repeat part (a) using appropriate mathematical technique.
c) Predict how far down range the missile will land.
Q.2. Plot the following data:
> t = [ 0 .1 .499 .5 .6 1.0 1.4 1.5 1.899 1.9 2.0]
> y = [ 0 .06 .17 .19 .21 .26 .29 .29 .30 .31 .31]
a) Try a polynomial fit of the correct degree to interpolate this number of data
points. What do you observe? Give an explanation of this error, in particular why
is the term badly conditioned used?
b) Plot the above data along with a spline interpolant. How does this compare with
the plot above?
c) What is a way to make the plot better?
Q.3. The upper portion of this noble beast is to be approximated using clamped cubic
spline interpolants. The curve is drawn on a grid from which the table is constructed.
Construct the three natural cubic splines and plot them on the same graph.
The Natural Spline:
Q.4. Find the unique least squares solutions of the following system of equations.
𝑥+𝑦 =1
−𝑥 + 2𝑦 = 0
3𝑥 + 4𝑦 = 6
Q.5. Find the unique minimum length least squares solutions of the following system of
equations.
𝑥 + 2𝑦 − 𝑧 = 3
−𝑥 + 𝑦 + 4𝑧 = −1