Matrix Decompositions: Linpack and Beyond

  • Charles F. Van Loan
  • Misha E. Kilmer
  • Dianne P. O’Leary
Part of the Contemporary Mathematicians book series (CM)


Stewart’s thesis advisor Alston Householder was a strong and effective advocate for using factorizations in explaining and in solving matrix problems [73]. Stewart adopted a similar viewpoint in his expository work; see [GWS-B1,GWS-B3], etc. Through his research, Stewart brought new theoretical insights into matrix factorizations and worked on definitive software implementations of factorization algorithms. In this chapter we focus on some of his key contributions to LU, QR, Cholesky, and singular value decompositions (SVD). Additional contributions to eigendecompositions, SVD, and updating of factorizations will be discussed in later chapters.


Singular Value Decomposition Matrix Decomposition Numerical Linear Algebra Sylvester Equation Householder Transformation 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Charles F. Van Loan
    • 1
  • Misha E. Kilmer
    • 2
  • Dianne P. O’Leary
    • 3
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA
  2. 2.Department of MathematicsTufts UniversityMedfordUSA
  3. 3.Computer Science Department and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA

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