Updating and Downdating Matrix Decompositions

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


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.


Singular Vector Cholesky Factor Plane Rotation Signal Subspace Noise Subspace 
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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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