Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Numerical stability From Wikipedia, the free encyclopedia Jump to: navigation, search This article includes a list of references, but In other contexts, for instance when solving differential equations, a different definition of numerical stability is used. 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 Your cache administrator is webmaster.

Please try the request again. They are related to some concept of stability in the dynamical systems sense, often Lyapunov stability. Error analysis (mathematics) From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, error analysis is the study of kind and quantity of error, or uncertainty, that may be present Your cache administrator is webmaster.

Often, we want the error to be of the same order as, or perhaps only a few orders of magnitude bigger than, the unit round-off. Contents 1 Error analysis in numerical modeling 1.1 Forward error analysis 1.2 Backward error analysis 2 Applications 2.1 Global positioning system 2.2 Molecular dynamics simulation 2.3 Scientific data verification 3 See The system returned: (22) Invalid argument The remote host or network may be down. Backward error propagation: How much error in input would be required to explain all output error?

Reilly(ed); David Hemmendinger(ed) (8 September 2003). "Error Analysis" in Encyclopedia of Computer Science. It has come to be widely used for navigation both by the U.S. Your cache administrator is webmaster. Stability is a measure of the sensitivity to rounding errors of a given numerical procedure; by contrast, the condition number of a function for a given problem indicates the inherent sensitivity

Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. The following definitions of forward, backward, and mixed stability are often used in numerical linear algebra. This issue is particularly prominent in applied areas such as numerical analysis and statistics. Springer.

ISBN978-0-470-86412-8. Modeling Biological Systems: Principles and Applications. Assumes that approximate solution to problem is good IF IT IS THE exact solution to a ``nearby'' problem. The result of the algorithm, say y*, will usually deviate from the "true" solutiony.

It is important to use a stable method when solving a stiff equation. McGraw-Hill Professional. Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Next: Stability and Accuracy Up: The Big Picture on Previous: Errors during computation: Backward Error Analysis See Figure 12 In numerical ordinary differential equations, various concepts of numerical stability exist, for instance A-stability.

Generated Sun, 16 Oct 2016 00:40:22 GMT by s_ac15 (squid/3.5.20) By using this site, you agree to the Terms of Use and Privacy Policy. An opposite phenomenon is instability. pp.186–189.

Rapaport, The Art of Molecular Dynamics Simulation, Cambridge University Press. Mixed stability combines the concepts of forward error and backward error. Some numerical algorithms may damp out the small fluctuations (errors) in the input data; others might magnify such errors. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Error_analysis_(mathematics)&oldid=695749582" Categories: Numerical analysisError Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Article Talk Variants Views Read Edit View history More Search Navigation Main pageContentsFeatured contentCurrent eventsRandom pp.50–. Your cache administrator is webmaster. In such situations we rewrite the variance as: σ 2 ( ⟨ A ⟩ ) = 1 M σ 2 A [ 1 + 2 ∑ μ ( 1 − μ

An algorithm is stable in this sense if it solves a nearby problem approximately, i.e., if there exists a Δx such that both Δx is small and f (x + Δx) − p.11. In many cases, it is more natural to consider the relative error | Δ x | | x | {\displaystyle {\frac {|\Delta x|}{|x|}}} instead of the absolute error Δx. Please try the request again.

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. The forward error of the algorithm is the difference between the result and the solution; in this case, Δy = y* − y. 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 ISBN 0-534-39200-8 Retrieved from "https://en.wikipedia.org/w/index.php?title=Numerical_stability&oldid=710811251" Categories: Numerical analysisHidden categories: CS1 maint: Multiple names: authors listArticles lacking in-text citations from February 2012All articles lacking in-text citations Navigation menu Personal tools Not logged

Please try the request again. The system returned: (22) Invalid argument The remote host or network may be down. The usual definition of numerical stability uses a more general concept, called mixed stability, which combines the forward error and the backward error. The backward error is the smallest Δx such that f (x + Δx) = y*; in other words, the backward error tells us what problem the algorithm actually solved.