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Quadratically constrained least squares and quadratic problems (1991)

Golub, Gene H. ; Matt, Urs

Springer

Numerische Mathematik 59 (1991), S. 561-580

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ISSN: 0945-3245

Keywords: 65F20

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary We consider the following problem: Compute a vectorx such that ∥Ax−b∥2=min, subject to the constraint ∥x∥2=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 ofx T A x−2b T x subject to the constraint ∥x∥2=α. Some numerical examples are given.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01385796

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