1) The following data define the sea-level concentration of dissolved oxygen for fresh water as a function of temperature:
|
T
|
0
|
8
|
16
|
24
|
32
|
40
|
|
01F
|
14.64
|
11.85
|
9.87
|
8.41
|
7.30
|
6.43
|
Use MATLAB to fit the data with
(a) piecessise linear interpolation,
(b) a fifth-order polynomial, and
(c) a spline.
Display the results graphically on one graph (label each properly and use different coloring schemes and different line types for each)
d) Use each approach to estimate 0(27). Note that the exact result is 7.986 mg/L. What is the percentage error in each case? (Supply your answers in a table similar to this below, and make sure you include all the details of your calculations).
Piecewise Fifth-order Spline
0(27
% Error = (true-estimate)/true
2) Use nonlinear regression to estimate a4 and (34 based on the following data. Develop a plot of your fit along with the data.
y = a4xe134'
|
X
|
0.1
|
0.2
|
0.4
|
0.6
|
0.9
|
1.3
|
1.5
|
1.7
|
1.8
|
|
y
|
0.75
|
1.25
|
1.45
|
1.25
|
0.85
|
0.55
|
0.35
|
0.28
|
0.17
|
|
3) Use a Lagrange interpolating polynomial of the second order to evaluate the density of unused motor oil at
x = 13, based on the following data. Show all your calculations in MATLAB.
xi = 0 f (xi) = 3.8
x, = 20 f (x2) = 0.8
x3 = 40 f (x3) = 0.2
|
|
4) Employ a second-order Newton polynomial to estimate y = log(x) at x = 2, with the following three points. Show all your calculations in MATLAB.
x1 = 1 f(xi) = 0
x2 = 4 f (x2) = 1.387
x3 = 6 f (x3) = 1.791
|