High precision numerical algorithms by finite fields
Project/Area Number |
26610039
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Multi-year Fund |
Research Field |
Foundations of mathematics/Applied mathematics
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Research Institution | Kobe University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2017-03-31
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Project Status |
Completed (Fiscal Year 2016)
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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)
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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.
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Report
(4 results)
Research Products
(8 results)