Computational aspects of Kolmogorov's superposition theorem

✍ Scribed by Hidefumi Katsuura; David A. Sprecher

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 454 KB
• Volume: 7
• Category: Article
• ISSN: 0893-6080
• DOI: 10.1016/0893-6080(94)90079-5

✦ Synopsis

This paper continues the investigation of representations of continuous functions f( X 1 ..... Xn) with n .... > 2 in the form f( x~, , Xn ) = ~ q=O2n Xqt a~ f z_,S" P=n I Xp ~b( Xp + qe,) ] with a predetermined function ~b that is independent of n. The fimction ~k is defined through its graph that is the limit point of iterated contraction mappings. The functions ~b and ¢bq are the uniform limits of sequences of computable functions constructed with a fixed mapping tr, which itself can be approximated with sigmoid functions.