2013 Fiscal Year Final Research Report
A Challenge to Relative Errors by Numerical Algorithms with Positivity
| Project/Area Number |
23654032
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 固有値計算 / 特異値計算 / 相対誤差 / 正値性 / 可積分アルゴリズム / 離散可積分系 / 漸近解析 / 行列式 |
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| Research Abstract |
In this project, we investigate the perturbations on singular values and the forward errors of the mdLVs variables, which occur in the mdLVs algorithm, through two kinds of error analysis in floating point arithmetic. Therefore the forward stability of the mdLVs algorithm is proved. Next we present a new similarity transformation named the dLV_\infty similarity transformation by considering the case where the discretization parameter \delta(n) goes to infinity in the integrable dLV system. It is proved that the singular values of bidiagonal matrix are computable by using the dLV_\infty transformation repeatedly. Therefore we clarify that the relative perturbations in the singular values are sufficiently small through the mixed forward-backward error analysis. We finally show that the dLV_\infty transformation is forward stable.
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