I wanted to comment on the solutions, but since I don't have 50 goo goo stars or whatever that are needed to be allowed to comment, I wanted to point out than when you're finding the max eigenvalue in the Markley method, I've found that the power iteration (https://en.wikipedia.org/wiki/Power_iteration) tends to be more robust than SVD with small rotations. At least with Eigen's JacobiSVD it crashes a lot.
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