컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0548 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Control Theory / Optimization (SS-13) |
| 영문제목 (Title(Eng.)) |
Hilbert's 13th problem and optimal compression of multidimensional numerical data |
| 저자(Author(s)) |
Shigeo Akashi1 Tokyo University of Science1 |
| 초록본문(Abstract) | It is famous that Kolmogorov and Arnold solved Hilbert's 13th problem asking if all continuous functions of several variables can be represented as superpositions of continuous functions of fewer variables. Actually, it is known that there exist several problems which have been derived from the original problem. For example, Vituskin solved the version of Hilbert's 13th problem for finitely differentiable functions, namely, the problem asking if, for any positive integers, $m, n, p$ and $q$, there exists a $q$-time differentiable function defined on $[0,1]^n$ which cannot be represented as any superpositions constructed from $p$-time differentiable functions defined on $[0,1]^m$, if $m/p < n/q$ holds. In this talk, we discuss the problem asking what extent superposition representation can be simplified to and apply this result to the optimal data compression of multidimensional numerical tables. |
| 분류기호 (MSC number(s)) |
26B40, 94A17 |
| 키워드(Keyword(s)) | Hilbert's 13th problem, superposition, data compression |
| 강연 형태 (Language of Session (Talk)) |
English |