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Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems

  • F. L. Bauer
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)

Abstract

Let A be a matrix of n rows and m columns, mn. If and only if the columns are linearly independent, then for any vector b there exists a unique vector x minimizing the Euclidean norm of \(b - Ax,\parallel b - Ax\parallel = \mathop {\min }\limits_\xi \parallel b - A\xi \parallel .\).

Keywords

Integer Matrix Iterative Improvement Elimination Step Orthogonalization Process Exact Inverse 
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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References

  1. [1]
    Bauer, F. L.: Optimally scaled matrices. Numer. Math. 5, 73 -87 (1963).MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Householder, A. S.: Principles of numerical analysis. New York 1953.Google Scholar
  3. [3]
    Golub, G. H.: Numerical methods for solving linear least squares problems. Numer. Math. 7, 206–216 (1965).MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Businger, P., and G. H. Golub. Linear least squares solutions by Householder transformations. Numer. Math. 7, 269–276 (1965). Cf. 1/9.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  • F. L. Bauer

There are no affiliations available

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