|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.
|Appears in Collections:||Publications without fulltext|
Show full item record
checked on May 29, 2023
checked on Jun 30, 2022
Add Files to Item
Note about this record
Cite this record
Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.