Application of Hilbert's 13th problem to lower dimensional decomposition of higher dimensional numerical tables

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400189
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokyo University of Science
• Principal Investigator: Akashi Shigeo 東京理科大学, 理工学部情報科学科, 教授 (30202518)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: ヒルベルトの第13問題 / 高次元データ / シンプソン公式 / DHCPスヌーピング / ネットワークセキュリティ / エントロピー / 多変数関数

Outline of Final Research Achievements

It is well known that the the theory of higher dimensional data compression is closely related to the theory of functions of several variables, because the 13th problem formulated by Hilbert in 1900 pointed out the way of decomposing functions of several variables into some functions of less several variables in the way of keeping reproducible would play important roles in the theory of nomographs, namely, graphs which are used to make numerical calculation without calculators much easier. The first result is to give a negative solution to the infinitely differentiable function version of the Hilbert's 13th problem and the second result is to develop a numerical-integration-oriented higher dimensional data decomposition. which can accelerate Simpson'approximate integration.

Free Research Field

エントロピー解析、情報理論、ネットワーク解析