Block computation and representation of a sparse nullspace basis of a rectangular matrix

Link:
Autor/in:
Verlag/Körperschaft:
Hamburg University of Technology
Erscheinungsjahr:
2008
Medientyp:
Text
Schlagworte:
  • Block QR factorization
  • Hierarchical matrices
  • Orthogonal factorization
  • 510: Mathematik
Beschreibung:
  • 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.
Beziehungen:
DOI 10.1016/j.laa.2007.11.025
Quellsystem:
TUHH Open Research
Interne Metadaten
Quelldatensatz
oai:tore.tuhh.de:11420/10617