Keywords
- Stationary Point
- Full Rank
- Descent Step
- Smooth Norm
- Haar Condition
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References
Anderson, D H and M R Osborne (1976). Discrete, linear approximation problems in polyhedral norms, Num. Math. 26, 179–189.
Anderson, D H and M R Osborne (1977a). Discrete, non-linear approximation problems in polyhedral norms, Num. Math. 28, 143–156.
Anderson, D H and M R Osborne (1977b). Discrete, non-linear approximation problems in polyhedral norms: a Levenberg-like algorithm. Num. Math. 28, 157–170.
Barrodale, I and F D K Roberts (1973). An improved algorithm for discrete ℓ1 linear approximation, SIAMJ Num. Anal. 10, 839–848.
Bartels, R H, A R Conn and J W Sinclair (1977). Minimisation techniques for piecewise differentiable functions — the ℓ1 solution to an over-determined linear system, SIAMJ Num. Anal. (to appear).
Cheney, E W (1966). Introduction to Approximation Theory, McGraw-Hill, New York.
Cline, A K (1976). A descent method for the uniform solution to overdetermined systems of linear equations, SIAMJ Num. Anal. 13, 293–309.
Fletcher, R, J A Grant and M D Hebden (1971). The calculation of linear best Lp approximations, Computer J. 14, 276–279.
Kelley, J E (Jr) (1958). An application of linear programming to curve fitting, SIAMJ 6, 15–22.
Madsen, K (1975). An algorithm for minimax solutions of overdetermined systems of non-linear equations, JIMA 16, 321–328.
Osborne, M R (1972). An algorithm for discrete, non-linear best approximation Problems: In: Numerische Methoden der Approximationstheorie, Band 1, eds. L Collatz and G Meinardus. Birkhauser-Verlag.
Osborne, M R (1977). Nonlinear least squares — the Levenberg algorithm revisited, J. Aust. Math. Soc., Series B (to appear).
Osborne, M R and G A Watson (1969). An algorithm for minimax approximation in the non-linear case, Computer J. 12, 64–69.
Osborne, M R and G A Watson (1971). On an algorithm for non-linear L1 approximation, Computer J. 14, 184–188.
Rockafellar, R T (1970). Convex Analysis, Princeton, New Jersey. Princeton Univ. Press.
Stiefel, E L (1959). Über diskrete und lineare Tschebyscheff-Approximationen, Num. Math. 1, 1–28.
Watson, G A (1974). The calculation of best restricted approximations, SIAMJ Num. Anal. 11, 693–699.
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© 1978 Springer-Verlag
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Osborne, M.R., Watson, G.A. (1978). Nonlinear approximation problems in vector norms. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067701
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DOI: https://doi.org/10.1007/BFb0067701
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