if b is changed to b + Δb (simulating, for example, errors in the data) then the corresponding change Δx in the solution satisfies
where cond(A) = ||A|| ||A–1|| is the condition number of A with respect to solving linear equations. The expression bounds the relative change in the solution in terms of the relative change in the data b. The actual quantities are measured in terms of a vector norm (see approximation theory). Similarly the condition number is expressed in terms of a corresponding matrix norm. It can be shown that cond(A)≥1. If cond(A) is large the problem is said to be ill-conditioned and it follows that a small relative change in b can lead to a large relative change in the solution x. This means that the accuracy of a computed approximation must be interpreted accordingly, taking into account the size of the possible data errors, machine precision, and errors induced by the particular algorithm.
Similar ideas apply to other problem areas and condition numbers feature in a measure of eigenvalue sensitivity in the matrix eigenvalue problem.
"condition number." A Dictionary of Computing. . Encyclopedia.com. (March 23, 2019). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/condition-number
"condition number." A Dictionary of Computing. . Retrieved March 23, 2019 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/condition-number
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.