Numerical Algorithms to compute common bases for symmetric commuting matrices

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I have a set of symmetric matrices $A_1,\dots,A_k \in \mathbb{R}^{n\times n}$ which commute with each other. This implies that they have a common eigenbasis. What are the best algorithms to find this bases given $A_1,\dots,A_k$? Ideally, these should be numerically stable.