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• Condition_number abstract "In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument. This is used to measure how sensitive a function is to changes or errors in the input, and how much error in the output results from an error in the input. Very frequently, one is solving the inverse problem – given one is solving for x, and thus the condition number of the (local) inverse must be used.The condition number is an application of the derivative, and is formally defined as the value of the asymptotic worst-case relative change in output for a relative change in input. The "function" is the solution of a problem and the "arguments" are the data in the problem. The condition number is frequently applied to questions in linear algebra, in which case the derivative is straightforward but the error could be in many different directions, and is thus computed from the geometry of the matrix. More generally, condition numbers can be defined for non-linear functions in several variables.A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned. The condition number is a property of the problem. Paired with the problem are any number of algorithms that can be used to solve the problem, that is, to calculate the solution. Some algorithms have a property called backward stability. In general, a backward stable algorithm can be expected to accurately solve well-conditioned problems. Numerical analysis textbooks give formulas for the condition numbers of problems and identify the backward stable algorithms.As a general rule of thumb, if the condition number , then you may lose up to digits of accuracy on top of what would be lost to the numerical method due to loss of precision from arithmetic methods. However, the condition number does not give the exact value of the maximum inaccuracy that may occur in the algorithm. It generally just bounds it with an estimate (whose computed value depends on the choice of the norm to measure the inaccuracy).".
• Condition_number wikiPageExternalLink mws_gen_sle_spe_adequacy.pdf.
• Condition_number wikiPageExternalLink Condition_number.
• Condition_number wikiPageExternalLink cond.html.
• Condition_number wikiPageID "6934".
• Condition_number wikiPageRevisionID "605616469".
• Condition_number hasPhotoCollection Condition_number.
• Condition_number id "3480".
• Condition_number title "Matrix condition number".
• Condition_number subject Category:Matrices.
• Condition_number subject Category:Numerical_analysis.
• Condition_number type Abstraction100002137.
• Condition_number type Arrangement107938773.
• Condition_number type Array107939382.
• Condition_number type Group100031264.
• Condition_number type Matrices.
• Condition_number type Matrix108267640.
• Condition_number comment "In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument. This is used to measure how sensitive a function is to changes or errors in the input, and how much error in the output results from an error in the input.".
• Condition_number label "Condition number".
• Condition_number label "Conditionnement (analyse numérique)".
• Condition_number label "Condizionamento (matematica)".
• Condition_number label "Kondition (Mathematik)".
• Condition_number label "Número de condicionamento".
• Condition_number label "Wskaźnik uwarunkowania".
• Condition_number label "Число обусловленности".
• Condition_number label "条件数".
• Condition_number label "条件数".
• Condition_number sameAs Podmíněnost_matice.
• Condition_number sameAs Kondition_(Mathematik).
• Condition_number sameAs Conditionnement_(analyse_numérique).
• Condition_number sameAs Condizionamento_(matematica).
• Condition_number sameAs 条件数.
• Condition_number sameAs 조건수.
• Condition_number sameAs Wskaźnik_uwarunkowania.
• Condition_number sameAs Número_de_condicionamento.
• Condition_number sameAs m.01_rm.
• Condition_number sameAs Q1147936.
• Condition_number sameAs Q1147936.
• Condition_number sameAs Condition_number.
• Condition_number wasDerivedFrom Condition_number?oldid=605616469.
• Condition_number isPrimaryTopicOf Condition_number.