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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.

UDC: 519.61

Received: 04.09.2015