The next problem of interpolation I do not know how to approach it. The problem says:
A way to interpolate in two dimensions the values of $f (x, y)$ in the vertices $(x_1, y_1)$, $(x_1, y_2)$, $(x_2, y_1), (x_2, y_2)$ of a rectangle, where we seek to approximate $f (x$ *$, y$ * $)$, is:
--Interpolate linearly between $f (x_1, y_1)$ and $f(x_2, y_1)$ giving $f_1$*$(x $ *$, y_1)$
--Interpolate linearly between $f (x_1, y_2)$ and $f(x_2, y_2)$ giving $f_2$*$(x $ *$, y_2)$
--Interpolate linearly between $f (x$* $, y_1)$ and $f(x$* $, y_2)$ giving $f$*$(x $ *$, y$ * $)$
This process can be done in reverse order, interpolating first in $y$ and then in $x$.
the questions are:
$a)$ Does the order in which the variables are considered refer? (If so, the method is at least suspect.)
$b)$ What does it correspond to, in terms of the multivariate polynomial used to interpolate?
Hint: Algebra is heavy, use a symbolic algebra package (like SymPy for Python).
in what way and with what arguments can I answer the request?