Geodesic
A parallel algorithm for the sparse QR decomposition of a rectangular upper quasi-triangular matrix with ND-type sparsity
Numerical methods and programming, Tome 16 (2015) no. 4, pp. 566-577.

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An algorithm for computing the sparse $QR$ decomposition of a specially ordered rectangular matrix is proposed. This decomposition is based on the block sparse Householder transformations. For ordering computations, the nested dissection ordering is used for the matrix $A^{T}A$, where $A$ is the original rectangular matrix. For mesh based problems, the ordering can be constructed starting from an appropriate volume partitioning of the computational mesh. Parallel computations are based on sparse $QR$ decomposition for sets of rows with an additional initial zero block.
Mots-clés : sparse rectangular matrix, $QR$ decomposition
Keywords: upper quasi-triangular matrix, volume partitioning, nested dissection, Householder transformations, parallel algorithm. 
@article{VMP_2015_16_4_a10,
     author = {S. A. Kharchenko},
     title = {A parallel algorithm for the sparse {QR} decomposition of a rectangular upper quasi-triangular matrix with {ND-type} sparsity},
     journal = {Numerical methods and programming},
     pages = {566--577},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2015_16_4_a10/}
}
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S. A. Kharchenko. A parallel algorithm for the sparse QR decomposition of a rectangular upper quasi-triangular matrix with ND-type sparsity. Numerical methods and programming, Tome 16 (2015) no. 4, pp. 566-577. http://geodesic.mathdoc.fr/item/VMP_2015_16_4_a10/