The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation

Year 2018, Volume: 1 Issue: 2, 58 - 64, 31.08.2018

Shigeo Akashi

Abstract

In this paper, it is proved that there exist polynomials of three complex variables which cannot be represented as any Kolmogorov-Arnold superposition, which has played important roles in the original version of Hilbert's 13th problem.

Keywords

Hilbert's 13th problem, superposition representation, $\varepsilon$-entropy

References

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