Geodesic
QR factorizations using a restricted set of rotations
Electronic transactions on numerical analysis, Tome 21 (2005), pp. 20-27.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Any matrix of dimension ( ) can be reduced to upper triangular form by multiplying $\sterling $#############$\ddot $§ ###$\copyright $§ by a sequence of appropriately chosen rotation matrices. In this work, we address the question $$###$$§§§! #"%$'\ of whether such a factorization exists when the set of allowed rotation planes is restricted. We introduce the rotation graph as a tool to devise elimination orderings in QR factorizations. Properties of this graph characterize sets of rotation planes that are sufficient (or sufficient under permutation) and identify rotation planes to add to complete a deficient set. We also devise a constructive way to determine all feasible rotation sequences for performing the QR factorization using a restricted set of rotation planes. We present applications to quantum circuit design and parallel QR factorization.$
Classification : 65F25, 81R05, 65F05, 65F20, 81P68
Keywords: QR decomposition, givens rotations, plane rotations, parallel QR decomposition, quantum circuit design, qudits 
@article{ETNA_2005__21__a7,
     author = {O'Leary, Dianne P. and Bullock, Stephen S.},
     title = {QR factorizations using a restricted set of rotations},
     journal = {Electronic transactions on numerical analysis},
     pages = {20--27},
     publisher = {mathdoc},
     volume = {21},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__21__a7/}
}
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O'Leary, Dianne P.; Bullock, Stephen S. QR factorizations using a restricted set of rotations. Electronic transactions on numerical analysis, Tome 21 (2005), pp. 20-27. http://geodesic.mathdoc.fr/item/ETNA_2005__21__a7/