| Project 4 - Interpolation of Vehicle Stopping Distances Using Newton Divided Difference Polynomials |
The following table contains vehicle stopping distances as a function of speed.
|
V (mph) |
D (ft) |
|
0 |
0 |
|
20 |
42 |
|
25 |
56 |
|
30 |
74 |
|
35 |
93 |
|
40 |
116 |
|
45 |
143 |
|
50 |
173 |
|
55 |
210 |
|
60 |
248 |
|
65 |
295 |
|
70 |
343 |
|
75 |
401 |
|
80 |
464 |
A) Use MATLAB to fit a 6th order Newton Divided Difference Interpolating Polynomial to the underlined data set, i.e. [(0,0), (25,56),......,(75,401)]. That is, find the coefficients bi, i=0,1,2,3,4,5,6 in
D6(v) = b0 + b1(v-v0) +
b2(v-v0)(v-v1) + ....+
b6(v-v0)(v-v1) ×
×
×
×
(v-v5)
The program must calculate and output all of the finite differences, i.e.
f(v0), f[v1,v0], f[v2,v1],......, f[v6,v5,v4,v3,v2,v1,v0] and label those which are equal to the coefficients b0, b1, ......, b6.
B) Use the results to interpolate the stopping distances for those speeds in the table which are not underlined, i.e. 20, 30, 40, 50, 60, 70 and for extrapolation of the stopping distance at 80 mph. Print the estimated and actual values for the stopping distance in a table.
C) Estimate the error in the interpolated stopping distance from a speed of 60 mph by including the additional data point (80,464) to obtain the 7th order polynomial D7(v). Use D7(60) - D6(60) as the estimated error.