BIT Numerical Mathematics

, Volume 42, Issue 2, pp 300–322

Incremental Norm Estimation for Dense and Sparse Matrices

  • Iain S. Duff
  • Christof Vömel

DOI: 10.1023/A:1021946924741

Cite this article as:
Duff, I.S. & Vömel, C. BIT Numerical Mathematics (2002) 42: 300. doi:10.1023/A:1021946924741


We present an incremental approach to 2-norm estimation for triangular matrices. Our investigation covers both dense and sparse matrices which can arise for example from a QR, a Cholesky or a LU factorization. If the explicit inverse of a triangular factor is available, as in the case of an implicit version of the LU factorization, we can relate our results to incremental condition estimation (ICE). Incremental norm estimation (INE) extends directly from the dense to the sparse case without needing the modifications that are necessary for the sparse version of ICE. INE can be applied to complement ICE, since the product of the two estimates gives an estimate for the matrix condition number. Furthermore, when applied to matrix inverses, INE can be used as the basis of a rank-revealing factorization.

Matrix norm condition number incremental estimators approximate singular vectors sparse triangular matrices QR factorization rank-revealing 

Copyright information

© Swets & Zeitlinger 2002

Authors and Affiliations

  • Iain S. Duff
    • 1
    • 2
  • Christof Vömel
    • 2
  1. 1.Atlas Centre, RALOxonEngland
  2. 2.CERFACS, 42ToulouseFrance

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