Page 179 - Applied Numerical Methods Using MATLAB

168 INTERPOLATION AND CURVE FITTING
50
1.5
0
–50 1.0
0 10 20 30 40 0 10 20 30 40
2
(0) y = ax + bx + c (a = 0.1, b = –1, c = –50) (1) y = a + b (a = 2, b = 1)
x
5
2
0
1
–5 0
0 10 20 30 40 0 10 20 30 40
b x
(2) y = (a = –20, b = –9) (3) y = a b (a = 2, b = 0.95)
x + a
60
2
40
1.5
20
0 1
0 10 20 30 40 0 10 20 30 40
ax
(4) y = b e (a = 0.1, b = 1) (5) y = C – b e –ax (a = 0.1, b = 1, C = 1)
4 0.5
2

0 0
0 10 20 30 40 0 10 20 30 40
b
b
(6a) y = a x (a = 0.5, b = 0.5) (6b) y = a x (a = 0.5, b = –0.5)
2
5
1
0 0
0 10 20 30 40 0 10 20 30 40
bx
(7) y = ax e (a = 0.5, b = −0.1) C = y(∞)
(8) y = (a = –0.2, b = 20, C = 5)
1 + b e ax
10 0
–5
5
–10
0 –15
0 10 20 30 40 0 10 20 30 40
(9a) y = a ln x + b (a = 2, b = 1) (9b) y = a ln x + b (a = –4, b = 1)
Figure P3.11 LS fitting curves for data pairs with various relations.
3.12 Two-Dimensional Interpolation

Compose a routine “z = find_depth(xi,yi)” that finds the depth z of a
geological stratum at a point (xi,yi) given as the input arguments, based
on the data in Problem 1.4.