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Updating and Downdating Matrix Decompositions

  • Lars Eldén
  • Misha E. Kilmer
  • Dianne P. O’Leary
Part of the Contemporary Mathematicians book series (CM)

Abstract

The Sherman–Morrison–Woodbury formula ([GWS-B7], p. 328) is a recipe for constructing the inverse of a matrix after it has been modified by a low-rank correction. For a matrix of size n ×n that has been so modified, it enables the inverse of this matrix to be updated in time proportional to kn, where k is the rank of the correction, rather than the n 3 time usually necessary to compute the inverse directly. This important fact has enabled a variety of algorithms, from early implementations of the simplex method for linear optimization [29] to algorithms for solving least squares problems when new data arrive.

Keywords

Singular Vector Cholesky Factor Plane Rotation Signal Subspace Noise Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Lars Eldén
    • 1
  • Misha E. Kilmer
    • 2
  • Dianne P. O’Leary
    • 3
  1. 1.Department of MathematicsLinköping UniversityLinköpingSweden
  2. 2.Department of MathematicsTufts UniversityMedfordUSA
  3. 3.Computer Science Department and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA

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