A two-dimensional table is given below. Use a linear interpolation to find (2.5, 3.5) where f(x, y) is given below:
y \ x
2
3
4
5
1
80
84
85
87
2
66
72
76
80
3
51
61
66
71
4
29
49
58
64
5
12
40
51
55
(i) Generalize the Lagrange interpolation algorithm to perform quadratic interpolations of functions of two variables.
(ii) Use the algorithm to find (2.5, 3.5) for the above table.
