APPROXIMATIVE VERSIONS OF KOLMOGOROVS SUPERPOSITION THEOREM, PROVED CONSTRUCTIVELY

[摘要] In this paper, we prove constructively two approximative versions of the superposition theorem of Kolmogorov (1963), corresponding to Lorentz (1962) and Sprecher (1965). The proofs are constructive in the sense that only rationals, expressible as finite decimal sums, are used. The approximations consist in algorithms with error bounds. Concerning their complexity, the two results differ in the way the occurring sequences are constructed: recursively, respectively explicitly.

[发布日期] 1994-09-30

[关键词] MULTIVARIATE APPROXIMATION;CONSTRUCTIVE;SUPERPOSITION