I have a linear system of the type
$$Ax = b$$
I want to minimise $|b - Ax|^2$. I know there are different approaches to directly solve the system (Normal equation + Cholesky, QR decomposition, SVD decomposition) that have different numerical stability.
I would like to ask how it is possible to estimate the impact of the numerical error on the estimates of each parameter $x$.
Can it be done solely on the base of the condition number?
Should it be done using Monte Carlo simulation?
How should such simulation be designed?