2016 Fiscal Year Final Research Report
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 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kobe University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 数値解析 / 有限体 |
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| 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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| Free Research Field |
数値解析
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