Exact Prediction of QR Fill-In by Row-Merge Trees

  • Authors:

  • Suely Oliveira

  • Affiliations:

  • -

  • Venue:
  • SIAM Journal on Scientific Computing
  • Year:
  • 2000

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Abstract

Row-merge trees for forming the QR factorization of a sparse matrix A are closely related to elimination trees for the Cholesky factorization of AT A. Row-merge trees predict the exact fill-in (assuming no numerical cancellation) provided A satisfies the strong Hall property, but overestimate the fill-in in general. However, here a fast and simple postprocessing step for row-merge trees is presented that predicts the exact fill-in for sparse QR factorization using Householder reflectors for general matrices.