Geodesic
A parallel QR-factorization/solver of quasiseparable matrices
Electronic transactions on numerical analysis, Tome 30 (2008), pp. 144-167
This manuscript focuses on the development of a parallel $QR$-factorization of structured rank matrices, which can then be used for solving systems of equations. First, we will prove the existence of two types of Givens transformations, named rank decreasing and rank expanding Givens transformations. Combining these two types of Givens transformations leads to different patterns for annihilating the lower triangular part of structured rank matrices. How to obtain different annihilation patterns, for computing the upper triangular factor $R$, such as the

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and pattern will be investigated. Another pattern, namely the -pattern, will be used for computing the $\textcent \sterling QR$-factorization in a parallel way.
Classification : 65F05
Keywords: parallel $QR$-factorization, structured rank matrices, quasiseparable matrix 
@article{ETNA_2008__30__a16,
     author = {Vandebril,  Raf and Van Barel,  Marc and Mastronardi,  Nicola},
     title = {A parallel {QR-factorization/solver} of quasiseparable matrices},
     journal = {Electronic transactions on numerical analysis},
     pages = {144--167},
     year = {2008},
     volume = {30},
     zbl = {1171.65017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__30__a16/}
}
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%A Mastronardi,  Nicola
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Vandebril,  Raf; Van Barel,  Marc; Mastronardi,  Nicola. A parallel QR-factorization/solver of quasiseparable matrices. Electronic transactions on numerical analysis, Tome 30 (2008), pp. 144-167. http://geodesic.mathdoc.fr/item/ETNA_2008__30__a16/