Validated numerics, or rigorous computation, verified computation, reliable computation, numerical verification (German: Zuverlässiges Rechnen) is numerics including mathematically strict error (rounding error, truncation error, discretization error) evaluation, and it is one field of numerical analysis. For computation, interval arithmetic is used, and all results are represented by intervals. Validated numerics were used by Warwick Tucker in order to solve the 14th of Smale's problems, and today it is recognized as a powerful tool for the study of dynamical systems.
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| - 精度保証付き数値計算 (ja)
- Validated numerics (en)
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| - 精度保証付き数値計算（せいどほしょうつきすうちけいさん、Validated Numerics, Rigorous Computation, Reliable Computation, Verified Computation, Numerical Verification, 独: Zuverlässiges Rechnen）とは数学的に厳密な誤差（前進誤差、後退誤差、丸め誤差、打切り誤差、離散化誤差）の評価を伴う数値計算のことであり、数値解析の一分野である。演算では区間演算を使用し、結果はすべて区間で出力する。精度保証付き数値計算はウォリック・タッカーによって14番目のスメイルの問題を解くのにも活用されており（を参照）、力学系の研究では重要なツールとして位置づけられている。 「数値解析」および「区間演算」も参照 (ja)
- Validated numerics, or rigorous computation, verified computation, reliable computation, numerical verification (German: Zuverlässiges Rechnen) is numerics including mathematically strict error (rounding error, truncation error, discretization error) evaluation, and it is one field of numerical analysis. For computation, interval arithmetic is used, and all results are represented by intervals. Validated numerics were used by Warwick Tucker in order to solve the 14th of Smale's problems, and today it is recognized as a powerful tool for the study of dynamical systems. (en)
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| - Validated numerics, or rigorous computation, verified computation, reliable computation, numerical verification (German: Zuverlässiges Rechnen) is numerics including mathematically strict error (rounding error, truncation error, discretization error) evaluation, and it is one field of numerical analysis. For computation, interval arithmetic is used, and all results are represented by intervals. Validated numerics were used by Warwick Tucker in order to solve the 14th of Smale's problems, and today it is recognized as a powerful tool for the study of dynamical systems.(See also: Numerical analysis and Interval arithmetic)
(en)
- 精度保証付き数値計算（せいどほしょうつきすうちけいさん、Validated Numerics, Rigorous Computation, Reliable Computation, Verified Computation, Numerical Verification, 独: Zuverlässiges Rechnen）とは数学的に厳密な誤差（前進誤差、後退誤差、丸め誤差、打切り誤差、離散化誤差）の評価を伴う数値計算のことであり、数値解析の一分野である。演算では区間演算を使用し、結果はすべて区間で出力する。精度保証付き数値計算はウォリック・タッカーによって14番目のスメイルの問題を解くのにも活用されており（を参照）、力学系の研究では重要なツールとして位置づけられている。 「数値解析」および「区間演算」も参照 (ja)
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