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- Numerical_stability abstract "In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues. On the other hand, in numerical algorithms for differential equations the concern is the growth of round-off errors and/or initially small fluctuations in initial data which might cause a large deviation of final answer from the exact solution.Some numerical algorithms may damp out the small fluctuations (errors) in the input data; others might magnify such errors. Calculations that can be proven not to magnify approximation errors are called numerically stable. One of the common tasks of numerical analysis is to try to select algorithms which are robust – that is to say, do not produce a wildly different result for very small change in the input data.An opposite phenomenon is instability. Typically, an algorithm involves an approximate method, and in some cases one could prove that the algorithm would approach the right solution in some limit. Even in this case, there is no guarantee that it would converge to the correct solution, because the floating-point round-off or truncation errors can be magnified, instead of damped, causing the deviation from the exact solution to grow exponentially.".
- Numerical_stability thumbnail Forward_and_backward_error.svg?width=300.
- Numerical_stability wikiPageID "233807".
- Numerical_stability wikiPageLength "6886".
- Numerical_stability wikiPageOutDegree "33".
- Numerical_stability wikiPageRevisionID "638663604".
- Numerical_stability wikiPageWikiLink Algorithms_for_calculating_variance.
- Numerical_stability wikiPageWikiLink Approximation_error.
- Numerical_stability wikiPageWikiLink Category:Numerical_analysis.
- Numerical_stability wikiPageWikiLink Chaos_theory.
- Numerical_stability wikiPageWikiLink Condition_number.
- Numerical_stability wikiPageWikiLink Differential_equation.
- Numerical_stability wikiPageWikiLink Dynamical_system.
- Numerical_stability wikiPageWikiLink Finite_difference_method.
- Numerical_stability wikiPageWikiLink Function_(mathematics).
- Numerical_stability wikiPageWikiLink Lax_equivalence_theorem.
- Numerical_stability wikiPageWikiLink Lyapunov_stability.
- Numerical_stability wikiPageWikiLink Machine_epsilon.
- Numerical_stability wikiPageWikiLink Mathematics.
- Numerical_stability wikiPageWikiLink Nicholas_Higham.
- Numerical_stability wikiPageWikiLink Nicholas_J._Higham.
- Numerical_stability wikiPageWikiLink Numerical_algorithm.
- Numerical_stability wikiPageWikiLink Numerical_analysis.
- Numerical_stability wikiPageWikiLink Numerical_diffusion.
- Numerical_stability wikiPageWikiLink Numerical_linear_algebra.
- Numerical_stability wikiPageWikiLink Numerical_methods_for_ordinary_differential_equations.
- Numerical_stability wikiPageWikiLink Numerical_partial_differential_equations.
- Numerical_stability wikiPageWikiLink Opposite_(semantics).
- Numerical_stability wikiPageWikiLink Order_of_magnitude.
- Numerical_stability wikiPageWikiLink Orders_of_magnitude.
- Numerical_stability wikiPageWikiLink Partial_differential_equation.
- Numerical_stability wikiPageWikiLink Relative_error.
- Numerical_stability wikiPageWikiLink Round-off_error.
- Numerical_stability wikiPageWikiLink Stability_theory.
- Numerical_stability wikiPageWikiLink Stiff_equation.
- Numerical_stability wikiPageWikiLink Total_variation.
- Numerical_stability wikiPageWikiLink Truncation_error.
- Numerical_stability wikiPageWikiLink Unit_round-off.
- Numerical_stability wikiPageWikiLink Von_Neumann_stability_analysis.
- Numerical_stability wikiPageWikiLink File:Forward_and_backward_error.svg.
- Numerical_stability wikiPageWikiLink File:Mixed_stability_diagram.svg.
- Numerical_stability wikiPageWikiLinkText "''stability''".
- Numerical_stability wikiPageWikiLinkText "Numerical stability".
- Numerical_stability wikiPageWikiLinkText "backward stability".
- Numerical_stability wikiPageWikiLinkText "backward stable".
- Numerical_stability wikiPageWikiLinkText "conditionally stable".
- Numerical_stability wikiPageWikiLinkText "multiplicative error".
- Numerical_stability wikiPageWikiLinkText "numerical error accumulation".
- Numerical_stability wikiPageWikiLinkText "numerical instabilities".
- Numerical_stability wikiPageWikiLinkText "numerical instability".
- Numerical_stability wikiPageWikiLinkText "numerical stability".
- Numerical_stability wikiPageWikiLinkText "numerically more stable".
- Numerical_stability wikiPageWikiLinkText "numerically stable".
- Numerical_stability wikiPageWikiLinkText "numerically unstable".
- Numerical_stability wikiPageWikiLinkText "stability of a numerical process".
- Numerical_stability wikiPageWikiLinkText "stability of numerical schemes".
- Numerical_stability wikiPageWikiLinkText "stability".
- Numerical_stability wikiPageWikiLinkText "stable algorithm".
- Numerical_stability wikiPageWikiLinkText "stable step length".
- Numerical_stability wikiPageWikiLinkText "stable".
- Numerical_stability wikiPageWikiLinkText "unstable".
- Numerical_stability hasPhotoCollection Numerical_stability.
- Numerical_stability wikiPageUsesTemplate Template:Math.
- Numerical_stability wikiPageUsesTemplate Template:More_footnotes.
- Numerical_stability wikiPageUsesTemplate Template:Mvar.
- Numerical_stability wikiPageUsesTemplate Template:Reflist.
- Numerical_stability subject Category:Numerical_analysis.
- Numerical_stability type Article.
- Numerical_stability type Algorithm.
- Numerical_stability type Article.
- Numerical_stability comment "In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation.".
- Numerical_stability label "Numerical stability".
- Numerical_stability sameAs استقرار_عددي.
- Numerical_stability sameAs Estabilitat_numèrica.
- Numerical_stability sameAs Stabilita_numerické_metody.
- Numerical_stability sameAs Stabilität_(Numerik).
- Numerical_stability sameAs Αριθμητική_ευστάθεια_αλγορίθμων.
- Numerical_stability sameAs Cifereca_stabileco.
- Numerical_stability sameAs Estabilidad_numérica.
- Numerical_stability sameAs Stabilité_numérique.
- Numerical_stability sameAs יציבות_נומרית.
- Numerical_stability sameAs Stabilità_numerica.
- Numerical_stability sameAs 数値的安定性.
- Numerical_stability sameAs Algorytm_numerycznie_stabilny.
- Numerical_stability sameAs Estabilidade_numérica.
- Numerical_stability sameAs m.01hzws.
- Numerical_stability sameAs Вычислительная_устойчивость.
- Numerical_stability sameAs Stabilita_numerickej_metódy.
- Numerical_stability sameAs عددی_ثبات.
- Numerical_stability sameAs Q1430640.
- Numerical_stability sameAs Q1430640.
- Numerical_stability sameAs 数值稳定性.
- Numerical_stability wasDerivedFrom Numerical_stability?oldid=638663604.
- Numerical_stability depiction Forward_and_backward_error.svg.
- Numerical_stability isPrimaryTopicOf Numerical_stability.