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Approximate functional complexity
Author(s):
R. C.
Buck
Journal:
Bull. Amer. Math. Soc.
81
(1975),
1112-1114.
MSC (1970):
Primary 41A30;
Secondary 26A72
MathSciNet review:
0387516
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Additional information
References:
- 1.
- V. I. Arnol'd, Representation of continuous functions of three variables by the superposition of continuous functions of two variables. Mat. Sb. 48 (90) (1959), 3-74;English transl., Amer. Math. Soc. Transl. (2) 28 (1963), 61-147. MR 22 #12191; 27 #3759. MR 153798
- 2.
- V. I. Arnol'd, Some questions on approximation and representation of functions, Proc. Internat. Congress Math., 1958, pp. 339-348; English transl., Amer. Math. Soc. Transl. (2) 53 (1966), 192-201. MR 22 #12192. MR 121454
- 3.
- V. I. Arnol'd, On the representability of a function of two variables in the form $\chi[\phi(x)+\psi(y)]$, Uspehi Mat. Nauk. 12 (1957), no. 2, (74), 119-121. (Russian) MR 19, 841. MR 90623
- 4.
- R. C. Buck, On approximation theory and functional equations, J. Approximation Theory 5 (1972), 228-237. MR 377363
- 5.
- A. N. Kolmogorov, On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition, Dokl. Akad. Nauk SSSR 114 (1957), 953-956; English transl., Amer. Math. Soc. Transl. (2) 28 (1963), 55-59. MR 22 #2669; 27 #3760. MR 111809
- 6.
- G. G. Lorentz, Metric entropy, widths, and superpositions of functions, Amer. Math. Monthly 69 (1962), 469-485. MR 25 #5323. MR 141926
- 7.
- D. A. Sprecher, Survey of solved and unsolved problems on superposition of functions, J. Approximation Theory 6 (1972), 122-134. MR 348347
- 8.
- A. G. Vituškin, Estimation of the complexity of the tabulation problem, Fizmatgiz, Moscow, 1959; English transl., Theory of the transmission and processing of information, Pergamon Press, New York and London, 1961. MR 22 #8265; 24 #A2187. MR 117486
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Additional Information:
DOI:
10.1090/S0002-9904-1975-13938-3
PII:
S 0002-9904(1975)13938-3
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