I have a function of several variables defined by k different couples. I want to invert it. I guess this is an inverse problem. But I don't know what to look for to solve it. Here is a more formal explanation of my problem:
Let f be a bijective function from $R^n$ to $R^n$. f is characterized by k different couples $[{(x1,x2,...xn),(y1,y2,...yn)}]_k$ verifying $f(x1,x2,...xn)=(y1,y2,...yn)$. For a given (y1,y2,...yn), calculate $f^{-1}(y1,y2,...n)$.
I calculate many couples $[{(x1,x2,...xn),(y1,y2,...yn)}]_k$ with finite element method. So I can only determine y from x. But I know this is a bijection. Then I stock this couples in a table. But I want to invert the table to obtain x from y.
What kind of method can be applied here ? Thank you.