2013 Fiscal Year Final Research Report
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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| 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 |
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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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[Remarks] 構築した多倍長計算ソフトウエアを http://www-an.acs.i.kyoto-u.ac.jp/~fujiwara/exflib で公開しており,ダウンロードして利用することができる.また区間演算による精度保証計算の一例として,数値的に不安定な問題として知られるHilbert行列の条件数を調べたものを http://www-an.acs.i.kyoto-u.ac.jp/~fujiwara/exflib/hilbert40.html に示している
