I have a code which has a large for loop (100,000 iterations) and I need to inverse these matrices in every loop
\begin{bmatrix} 1&x_1&x_1^2&y_1&y_1^2\\ 1&x_2&x_2^2&y_2&y_2^2\\ 1&x_3&x_3^2&y_3&y_3^2\\ 1&x_4&x_4^2&y_4&y_4^2\\ 1&x_5&x_5^2&y_5&y_5^2\\ \end{bmatrix}
\begin{bmatrix} 1&x_1&x_1^2&y_1&y_1^2&z_1&z_1^2\\ 1&x_2&x_2^2&y_2&y_2^2&z_2&z_2^2\\ 1&x_3&x_3^2&y_3&y_3^2&z_3&z_3^2\\ 1&x_4&x_4^2&y_4&y_4^2&z_4&z_4^2\\ 1&x_5&x_5^2&y_5&y_5^2&z_5&z_5^2\\ 1&x_6&x_6^2&y_6&y_6^2&z_6&z_6^2\\ 1&x_7&x_7^2&y_7&y_7^2&z_7&z_7^2\\ \end{bmatrix}
Is there another (special case) method other than (or including) standard method factorization or iterative methods that is the fastest and accurate way to invert these specific matrices with numerical values $x_i$,$y_i$, and assuming these matrices are invertible?
I studied briefly and found out that these are similar to Vandermonde matrices with two and three variables.
Here is one of the sources (http://www-users.math.umn.edu/~olver/n_/mv.pdf) where they discussed the LU factorization of block matrices in the form of Vandermonde matrices.
Referring to other relevant textbooks or research papers is also highly appreciated.
Edit:
After some research, there are some transformation matrix $W$ such that $WX$ is an SDD matrix (but for some $x, y, z$ values it is not SDD) and I used iterative solvers with roughly on an average of $35$ iterations to solve $5\times 5$ matrix. But few times it diverges.
That's why I would like to know a robust and fastest way to inverse these matrices in every loop.