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Strong uniqueness and second order convergence in nonlinear discrete approximation. (English) Zbl 0486.65008


MSC:

65D15 Algorithms for approximation of functions
65K05 Numerical mathematical programming methods
41A50 Best approximation, Chebyshev systems
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References:

[1] Anderson, D.H., Osborne, M.R.: Discrete linear approximation problems in polyhedral norms. Numer. Math.26, 179-189 (1976) · Zbl 0335.65003 · doi:10.1007/BF01395971
[2] Anderson, D.H., Osborne, M.R.: Discrete nonlinear approximation problems in polyhedral norms. Numer. Math28, 143-156 (1977) · Zbl 0342.65004 · doi:10.1007/BF01394449
[3] Cheney, E.W.: Introduction to approximation theory. New York: McGraw-Hill 1966 · Zbl 0161.25202
[4] Crome, L.: Strong uniqueness. A far reaching criterion for the convergence analysis of iterative procedures. Numer. Math.,29, 179-194 (1978) · Zbl 0352.65012 · doi:10.1007/BF01390337
[5] Fiacco, A.V., McCormick, G.P.: Nonlinear programming: sequential unconstrained minimization techniques New York: Wiley 1968 · Zbl 0193.18805
[6] Jittorntrum, K.; Sequential algorithms in nonlinear programming, Ph.D. Thesis, Australian National University, 1978 · Zbl 0403.65026
[7] Luenberger, D.G.: Optimisation by vector space methods. New York: Wiley 1968 · Zbl 0184.44502
[8] Osborne, M.R.: An algorithm for discrete, nonlinear, best approximation problems. In: Numerische Methoden der Approximationstheorie, Band 1. L. Collatz, G. Meinardus, (Hrsg.). Basel-Stuttgart: Birkh?user-Verlag 1972 · Zbl 0245.65006
[9] Osborne, M.R., Watson, G.A.: Nonlinear approximation in vector norms. In: numerical analysis, G.A. Watson, (ed.) Lecture Notes in Mathematics No. 630, pp. 117-133. Berlin-Heidelberg-New York: Springer 1978 · Zbl 0384.65030
[10] Rockafellar, R.T.: Convex analysis, Princeton: Princeton University Press, 1970 · Zbl 0193.18401
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