Publisher DOI: 10.1016/j.laa.2007.11.025
Title: Block computation and representation of a sparse nullspace basis of a rectangular matrix
Language: English
Authors: Le Borne, Sabine  
Keywords: Block QR factorization; Hierarchical matrices; Orthogonal factorization
Issue Date: 25-Jan-2008
Publisher: American Elsevier Publ.
Source: Linear Algebra and Its Applications 428 (11-12): 2455-2467 (2008-06-01)
Abstract (english): 
In this paper, we propose a new method to efficiently compute a representation of an orthogonal basis of the nullspace of a sparse matrix operator BT with B ∈ Rn × m, n > m. We assume that B has full rank, i.e., rank(B) = m. It is well-known that the last n - m columns of the orthogonal matrix Q in a QR factorization B = QR form such a desired null basis. The orthogonal matrix Q can be represented either explicitly as a matrix, or implicitly as a matrix H of Householder vectors. Typically, the matrix H represents the orthogonal factor much more compactly than Q. We will employ this observation to design an efficient block algorithm that computes a sparse representation of the nullspace basis in almost optimal complexity. This new algorithm may, e.g., be used to construct a null space basis of the discrete divergence operator in the finite element context, and we will provide numerical results for this particular application. © 2007 Elsevier Inc. All rights reserved.
ISSN: 0024-3795
Document Type: Article
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