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Overdetermined Systems of Linear Equations

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Encyclopedia of Optimization

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References

  1. Armstrong RD, Frome EL, Kung DS (1979) A revised simplex algorithm for the absolute deviation curve fitting problem. Comm Statist–Simula Computa 8:175–190

    Google Scholar 

  2. Barrodale I, Phillips C (1974) An improved algorithm for discrete Chebyshev linear approximation. In: Hartnell BL, Williams HC (eds) Proc. Fourth Manitoba Conf. Numer. Math. Utilitas Math. Pub., pp 177–190

    Google Scholar 

  3. Barrodale I, Phillips C (1975) Algorithm 495: solution of an overdetermined system of linear equations in the Chebyshev norm. ACM Trans Math Softw 1:264–270

    MATH  Google Scholar 

  4. Barrodale I, Roberts FDK (1973) An improved algorithm for discrete linear ℓ1 approximation. SIAM J Numer Anal 10:839–848

    MathSciNet  MATH  Google Scholar 

  5. Bartels RH, Conn AR, Charalambous C (1978) On Cline's direct method for solving overdetermined linear systems in the ℓ∞ sense. SIAM J Numer Anal 15:255–270

    MathSciNet  MATH  Google Scholar 

  6. Bartels RH, Conn AR, Sinclair JW (1978) Minimisation techniques for piecewise differentiable functions: the ℓ1 solution to an overdetermined linear system. SIAM J Numer Anal 15:224–241

    MathSciNet  MATH  Google Scholar 

  7. Bartels RH, Golub GH (1968) Stable numerical methods for obtaining the Chebyshev solution to an overdetermined system of equations. Comm ACM 11:401–406

    MathSciNet  Google Scholar 

  8. Björk A (1996) Numerical methods for least squares problems. SIAM, Philadelphia

    Google Scholar 

  9. Huber PJ (1981) Robust statistics. Wiley, New York

    MATH  Google Scholar 

  10. Joe B, Bartels RH (1983) An exact penalty method for constrained, discrete, linear ℓ∞ data fitting. SIAM J Sci Comput 4:69–84

    MathSciNet  MATH  Google Scholar 

  11. Li W, Swetits J (1998) Linear ℓ1 estimator and Huber M-estimator. SIAM J Optim 8

    Google Scholar 

  12. Madsen K, Nielsen HB (1993) A finite smoothing algorithm for linear ℓ1 estimation. SIAM J Optim 3:223–235

    MathSciNet  MATH  Google Scholar 

  13. Madsen K, Nielsen HB, Pinar MČ (1994) New characterizations of ℓ1 solutions to overdetermined systems of linear equations. Oper Res Lett 16:159–166

    MathSciNet  MATH  Google Scholar 

  14. Narula SC (1982) Optimization techniques in linear regression: A review. Optimization in Stat. In: TIMS/Studies Management Sci, vol 19, pp 11–29

    Google Scholar 

  15. Pinar MČ, Elhedhli S (1998) A penalty continuation method for the ℓ∞ solution of overdetermined linear systems. BIT 38:127–150

    MathSciNet  MATH  Google Scholar 

  16. Schryer N (1998) via G.H. Golub, Email: golub@sccm.stanford.edu

    Google Scholar 

  17. Watson GA (1980) Approximation theory and numerical methods. Wiley, New York

    MATH  Google Scholar 

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© 2008 Springer-Verlag

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Pĭnar, M.Ç. (2008). Overdetermined Systems of Linear Equations . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_496

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