Separators and structure prediction in sparse orthogonal factorization

  title={Separators and structure prediction in sparse orthogonal factorization},
  author={John R. Gilbert and Esmond G. Ng and Barry W. Peyton},
Abstract In the factorization A = QR of a sparse matrix A , the orthogonal matrix Q can be represented either explicitly (as a matrix) or implicitly (as a sequence of Householder vectors). A folk theorem states that the Householder vectors are much sparser than Q in practice. In this paper we make this folk theorem precise: we prove tight upper and lower bounds on the nonzero counts of the two representations in terms of the quality of separators in the column intersection graph of A . We… CONTINUE READING