On the Study of Symbolic-Numeric Computation Using Randomized and/or Approximation Algorithms

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K11760
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60010:Theory of informatics-related
• Research Institution: Tokyo University of Science
• Principal Investigator: Sekigawa Hiroshi 東京理科大学, 理学部第一部応用数学科, 教授 (00396178)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: 数値数式融合計算 / 近似アルゴリズム / 多項式の合成 / メビウス変換 / 凸結合 / ボロノイ図

Outline of Final Research Achievements

Symbolic-numeric computation is a computing methodology that has high reliability of symbolic computation, and efficiency and flexibility of numeric computation. We carried out research on efficient symbolic-numeric computation utilizing approximation algorithms. Our main results are algorithms computing approximate decomposition of polynomials and their application for polynomial evaluation. Some other results include an algorithm to compute the nearest convex combination of Moebius transformations for a given linear combination of them and an algorithm to find the sites of a given Vonoroi diagram whose sites are unknown.

Free Research Field

数値数式融合計算

Academic Significance and Societal Importance of the Research Achievements

計算機により数学的な計算を行う代表的な方法には数値計算と数式処理の二つがあり、この二つの方法は長所、短所が相補的である。そこで、数式処理に数値計算の手法や考え方をうまく利用し、数式処理と数値計算の長所を合わせもつ数値数式融合計算という計算方法が研究されている。本研究の成果は数値数式融合計算の効率化、新しい利用法であり、様々な分野における数学的な計算への利用が期待できる。