Geodesic
Differentiating matrix orthogonal transformations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1460-1473

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New numerical algorithms for differentiating matrix orthogonal transformations are constructed. They do not require that the derivatives of the orthogonal transformation matrix be available. An example is given how these algorithms can be applied to the numerically stable calculation of a solution to the discrete-time matrix Riccati sensitivity equation. 
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     author = {M. V. Kulikova and J. V. Tsyganova},
     title = {Differentiating matrix orthogonal transformations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1460--1473},
     publisher = {mathdoc},
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     number = {9},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a1/}
}
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M. V. Kulikova; J. V. Tsyganova. Differentiating matrix orthogonal transformations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1460-1473. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a1/