High-accurate Numerical Methods for Inverse Problems on Next-generation Computing Environments
| Project/Area Number |
23740075
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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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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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 多倍長計算 / 正則化法 / 数値的不安定性 / 非適切問題 / 高精度シュミレーション / 多倍長数値計算 / 高精度シミュレーション |
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| Research Abstract |
We have realized a high-accurate numerical computations for numerically unstable problems which arize in inverse or ill-posed problems. Our method consists of multiple-precision arithmetic, regularization scheme, and high-accurate discretization rules based on the theory of reproducing kernels. We also make examples where numerical solutions diverge under stable schemes due to accumulation of rounding errors. This means that theoretical stability of numerical schemes does not equivalent to the reliability of numerical solutions.
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Report
(4 results)
Research Products
(52 results)
