numerical and mathematical stabilities in fundamental symbolic-numeric computations
Project/Area Number |
15K00016
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Theory of informatics
|
Research Institution | Kobe University |
Principal Investigator |
Nagasaka Kosaku 神戸大学, 人間発達環境学研究科, 准教授 (70359909)
|
Project Period (FY) |
2015-04-01 – 2020-03-31
|
Project Status |
Discontinued (Fiscal Year 2019)
|
Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2019: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2018: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
Keywords | アルゴリズム / 数式処理 / 最大公約因子 / 近似最大公約因子 / 近似GCD / 数値・数式融合計算 / 構造化行列 |
Outline of Final Research Achievements |
Symbolic-numeric computations are used in the case where the given algebraic expression has a priori error, or for solving the given non-numeric problem by some numerical methods. In this project, we had studied numerical and mathematical stabilities in fundamental symbolic-numeric computations used in many algorithms. Our contributions are as follows. 1) we built a better performance framework that covers and interchanges known approximate GCD algorithms, 2) we published its implementations, 3) we gave the theory of parametric greatest common divisors by means of comprehensive Groebner systems (CGS), and 4) we applied them to approximate squarefree decomposition.
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Academic Significance and Societal Importance of the Research Achievements |
数値数式融合計算を含む計算機代数分野は,計算機に直接数学の問題を解かせる場合に必要とされ,理工系分野の理論研究から実践現場までの幅広い領域において必要不可欠なツールとなっている。本研究課題では,多様なアルゴリズムが存在する近似GCDに対し,統一した枠組みを用意することで比較検討やさらなる効率化を可能とさせたこと,工学的な設計などに表れる設計パラメータを含んだままの問題に適用可能な,パラメータを含むGCD計算アルゴリズムを提案したこと,などにより必要不可欠なツールの機能を大きく拡張した意義をもつ。
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Report
(5 results)
Research Products
(16 results)