• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

High precision numerical algorithms by finite fields

Research Project

Project/Area Number 26610039
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKobe University

Principal Investigator

Takayama Nobuki  神戸大学, 理学研究科, 教授 (30188099)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords数値解析 / 有限体 / 高精度計算 / 常微分方程式 / modular method / 超幾何多項式 / Runge-Kutta 法 / 超幾何関数
Outline of Final Research Achievements

We give numerical analysis algorithms and implementations for the following problems over the rational number fields, which give high precision numerical outputs. (1) fast evaluation method of iterations of linear transformations by a modular arithmetic and a distributed computation. (2) an efficient variation of the Bulirsch-Stoer method to solve linear ordinary differential equations numerically over rational numbers. An application of (1) is an exact evaluation of A-hypergeometric polynomial. An application of (2) is a numerical analysis near singular points of linear ordinary differential equations.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (8 results)

All 2017 2016 2015 2014 Other

All Journal Article (2 results) Presentation (4 results) Remarks (2 results)

  • [Journal Article] 2元分割表に対する差分ホロノミック勾配法の実装2017

    • Author(s)
      橘義仁, 後藤良彰, 高山信毅
    • Journal Title

      数理研考究録

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
  • [Journal Article] 2元分割表に対する差分ホロノミック勾配法の実装2016

    • Author(s)
      後藤良彰, 橘義仁, 高山信毅
    • Journal Title

      数理研講究録

      Volume: 未定

    • Related Report
      2015 Research-status Report
  • [Presentation] 常微分(差分)方程式用有理数対応数値解析パッケージ2017

    • Author(s)
      高山信毅
    • Organizer
      Risa/Asir Conference 2017
    • Place of Presentation
      金沢大学
    • Year and Date
      2017-03-28
    • Related Report
      2016 Annual Research Report
  • [Presentation] 2元分割表の条件付き確率の差分HGMによる計算2016

    • Author(s)
      高山信毅
    • Organizer
      日本数学会2016年度年会
    • Place of Presentation
      筑波大学(茨城県、つくば市)
    • Year and Date
      2016-03-17
    • Related Report
      2015 Research-status Report
  • [Presentation] Sylvester 型行列による超幾何関数の数値評価 --- グレブナー基底を使わない方法2015

    • Author(s)
      高山信毅
    • Organizer
      Risa/Asir Conference 2015
    • Place of Presentation
      金沢大学
    • Year and Date
      2015-03-18
    • Related Report
      2014 Research-status Report
  • [Presentation] 多変数超幾何関数の数値計算とその応用2014

    • Author(s)
      高山信毅
    • Organizer
      第八回玉原特殊多様体研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2014-09-17
    • Related Report
      2014 Research-status Report
  • [Remarks] 常微分(差分)方程式用有理数対応数値解析パッケージ

    • URL

      http://www.math.kobe-u.ac.jp/HOME/taka/2016/20170328-ohp-takayama.pdf

    • Related Report
      2016 Annual Research Report
  • [Remarks] Risa/Asir

    • URL

      http://www.math.kobe-u.ac.jp/Asir

    • Related Report
      2016 Annual Research Report

URL: 

Published: 2014-04-04   Modified: 2018-03-22  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi