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See for instance (3.13) in Higham's Accuracy and Stability of Numerical Algorithms: if $C=AB$ and $\hat{C}$ is its computed version, then $$ |C-\hat{C}| \leq \gamma_n |A|\,|B|, $$ where the absolute values …

The first thing you can do is determining the convergence rate experimentally. To do it, it is enough to plot error vs. iteration in a log-log scale and check the slope of the line that connects the i …

Technically speaking, it does not affect the numerical stability of that algorithm, but it modifies the problem to a more well-conditioned one, from $\min \|\Phi \theta - y\|^2$ to $$\min \|\Phi \theta …

If your inputs are $x,y,z$, this computation is not unstable, but ill-conditioned. That's worse, because it means that a small change in your input (such as a previous approximation as a floating-poin …

(1) [EDIT: fixed significantly with respect to the first version] Let $\lambda$ be an eigenvalue of $A$, and $\tilde{\lambda}$ the closest eigenvalue of a perturbed matrix $A+E$. If $A=VDV^{-1}$ is di …