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I'm looking for a formula to interpolate between two given matrices from the Stiefel manifold (orthogonal n by k matrices).

I do not know the tangent direction, I only know the start and end points so I'm not sure if formulas requiring the tangent vector to the Stiefel manifold can be used.

So far, I have looked at the paper by Edelman et al and Huper's "Rolling Stiefel manifolds".

Thanks.

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  • $\begingroup$ I am not entirely certain about the meaning of "interpolation" in this context. Are you looking for a curve connecting the two given points? $\endgroup$
    – Peter Crooks
    Commented Jan 1, 2014 at 16:16
  • $\begingroup$ You mean a geodesic? $\endgroup$
    – Federico Poloni
    Commented Jan 1, 2014 at 16:28
  • $\begingroup$ Yes. I am looking for a curve connecting two given orthonormal matrices, where all points on this curve are also orthonormal matrices. I think the easiest way is to linearly interpolate, between these two matrices, and then do a QR factorization of this intermediate matrix, and take the Q factor. $\endgroup$
    – codethink
    Commented Jan 1, 2014 at 16:39
  • $\begingroup$ @ Poloni Yes, a geodesic. But I don't know the tangent direction. Only the start and end. $\endgroup$
    – codethink
    Commented Jan 1, 2014 at 16:40

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