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Numerische Mathematik

, Volume 17, Issue 5, pp 387–401 | Cite as

Least squares algorithms for finding solutions of overdetermined linear equations which minimize error in an abstract norm

  • V. P. Sreedharan
Article

Abstract

In this paper overdetermined linear equations inn unknowns are considered. Ifm is the number of equations, let ℝ m be equipped with a smooth strictly convex norm, ‖·‖. Algorithms for finding “best-fit” solutions of the system which minimize the ‖·‖-error are given. The algorithms are iterative and in particular apply to the important case where ℝ m is given thel p -norms, (1<p<∞). The algorithms consist of obtaining a least square solution i.e. carrying out an orthogonal projection at each stage of the iteration and solving a non-linear equation in a single real variable. The convergence of the algorithms are proved in the paper.

Keywords

Linear Equation Mathematical Method Orthogonal Projection Real Variable Important Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • V. P. Sreedharan
    • 1
  1. 1.Department of MathematicsMichigan State UniversityE. LansingUSA

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