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Encyclopedia of Optimization pp 1856–1866Cite as

Least Squares Problems

  • Reference work entry

  • 547 Accesses

Article Outline

Keywords

Synonyms

Introduction

  Historical Remarks

  Statistical Models

  Characterization of Least Squares Solutions

Pseudo-inverse and Conditioning

  Singular Value Decomposition and Pseudo-inverse

  Conditioning of the Least Squares Problem

Numerical Methods of Solution

  The Method of Normal Equations

  Least Squares by QR Factorization

  Rank-Deficient and Ill-Conditioned Problems

  Rank Revealing QR Factorizations

Updating Least Squares Solutions

  Recursive Least Squares

  Modifying Matrix Factorizations

Sparse Problems

  Banded Least Squares Problems

  Block Angular Form

  General Sparse Problems

See also

References

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Author information

Authors and Affiliations

  1. Linköping University, Linköping, Sweden

    Åke Björck

Authors
  1. Åke Björck
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Björck, Å. (2008). Least Squares Problems . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_329

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