An alternative way of solving rotational Procrutes problem

[FanwangM]

An interesting paper proposed to solve the rotational Procrustes problem without SVD, J. Geom. Symmetry Phys., 53, 21–53, 2019. We can support this in the next major release.

[PaulWAyers]

@fwmeng88 is this different from:
#42
and
#16

It seems to be attempting something similar, but I didn't read the paper in detail.

[FanwangM]

I don't think the method proposed in this paper is related to #42 and #16. They provided an alternative way to solve rotational Procrustes problem 2D and 3D without doing SVD. page 17-28 in https://arxiv.org/pdf/1908.08824.pdf

@PaulWAyers

[PaulWAyers]

Ah, now I understand. The algorithm is interesting, but, as they note at the end, isn't really faster that SVD, so since the solution is the same we shouldn't expect anything different. It would be a sensible alternative algorithm that we could invoke when brute-force SVD is too costly, which would be interesting to have as a fallback in the long run. I think that in favorable cases, it seems, the new algorithm is faster.

[FanwangM]

Thanks for the clarification!