Numerische Mathematik

, Volume 59, Issue 1, pp 561–580 | Cite as

Quadratically constrained least squares and quadratic problems

  • Gene H. Golub
  • Urs von Matt


We consider the following problem: Compute a vectorx such that ∥Ax−b2=min, subject to the constraint ∥x2=α. A new approach to this problem based on Gauss quadrature is given. The method is especially well suited when the dimensions ofA are large and the matrix is sparse.

It is also possible to extend this technique to a constrained quadratic form: For a symmetric matrixA we consider the minimization ofxTAx−2bTx subject to the constraint ∥x2=α.

Some numerical examples are given.

Mathematics Subject Classification (1991)



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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Gene H. Golub
    • 1
  • Urs von Matt
    • 2
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA
  2. 2.Institut für Wissenschaftliches RechnenETH ZentrumZürichSwitzerland

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