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Num. Meth. Prog., 2015, Volume 16, Issue 4, Pages 566–577 (Mi vmp565)  

This article is cited in 1 scientific paper (total in 1 paper)

A parallel algorithm for the sparse QR decomposition of a rectangular upper quasi-triangular matrix with ND-type sparsity

S. A. Kharchenko

TESIS Company, Moscow

Abstract: 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.

Keywords: sparse rectangular matrix, upper quasi-triangular matrix, volume partitioning, nested dissection, $QR$ decomposition, Householder transformations, parallel algorithm.

Full text: PDF file (585 kB)
UDC: 519.61
Received: 04.09.2015

Citation: S. A. Kharchenko, “A parallel algorithm for the sparse QR decomposition of a rectangular upper quasi-triangular matrix with ND-type sparsity”, Num. Meth. Prog., 16:4 (2015), 566–577

Citation in format AMSBIB
\Bibitem{Kha15}
\by S.~A.~Kharchenko
\paper A parallel algorithm for the sparse QR decomposition of a rectangular upper quasi-triangular matrix with ND-type sparsity
\jour Num. Meth. Prog.
\yr 2015
\vol 16
\issue 4
\pages 566--577
\mathnet{http://mi.mathnet.ru/vmp565}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Kharchenko, A. A. Yuschenko, “Parallelnaya realizatsiya algoritma razrezhennogo QR razlozheniya dlya pryamougolnykh verkhnikh kvazitreugolnykh matrits so strukturoi razrezhennosti tipa vlozhennykh sechenii”, Vestn. YuUrGU. Ser. Vych. matem. inform., 5:2 (2016), 30–42  mathnet  crossref  elib
  • Numerical methods and programming
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