Article Outline
Keywords
See also
References
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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
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
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
Barrodale I, Roberts FDK (1973) An improved algorithm for discrete linear ℓ1 approximation. SIAM J Numer Anal 10:839–848
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
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
Bartels RH, Golub GH (1968) Stable numerical methods for obtaining the Chebyshev solution to an overdetermined system of equations. Comm ACM 11:401–406
Björk A (1996) Numerical methods for least squares problems. SIAM, Philadelphia
Huber PJ (1981) Robust statistics. Wiley, New York
Joe B, Bartels RH (1983) An exact penalty method for constrained, discrete, linear ℓ∞ data fitting. SIAM J Sci Comput 4:69–84
Li W, Swetits J (1998) Linear ℓ1 estimator and Huber M-estimator. SIAM J Optim 8
Madsen K, Nielsen HB (1993) A finite smoothing algorithm for linear ℓ1 estimation. SIAM J Optim 3:223–235
Madsen K, Nielsen HB, Pinar MČ (1994) New characterizations of ℓ1 solutions to overdetermined systems of linear equations. Oper Res Lett 16:159–166
Narula SC (1982) Optimization techniques in linear regression: A review. Optimization in Stat. In: TIMS/Studies Management Sci, vol 19, pp 11–29
Pinar MČ, Elhedhli S (1998) A penalty continuation method for the ℓ∞ solution of overdetermined linear systems. BIT 38:127–150
Schryer N (1998) via G.H. Golub, Email: golub@sccm.stanford.edu
Watson GA (1980) Approximation theory and numerical methods. Wiley, New York
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
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
Download citation
DOI: https://doi.org/10.1007/978-0-387-74759-0_496
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering