So lets say that I need to invert a matrix that is generally dense and is poorly conditioned. What are some ways I can get an accurate inverse?
Here are my candidates:
- SVD Inverse
- Inverse Via Cholesky Decomposition
- Inverse Via LU Decomposition
- Inverse Via QR Decomposition
Are there any other methods I am missing? Of all of them, which is the most robust to ill-conditioning? And why?
My thought is that it has to do with operation count. The smaller the number of operations needed, the less ability for error to propagate. So the most 'stable' methods are the ones with the lowest operation counts.
Edit: I only want to find the inverse of the matrix, not actually solve a linear system.