Condition number: Difference between revisions
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The condition number for a function <math>f</math> at a point <math>x_0</math> in the interior of its domain can be defined formally as: | The condition number for a function <math>f</math> at a point <math>x_0</math> in the interior of its domain can be defined formally as: | ||
<math>\lim \sup_{x \to x_0} \left| \frac{\frac{f(x) - f(x_0)}{f(x_0)}}{\frac{(x - x_0}{x_0}}\right|</math> | <math>\lim \sup_{x \to x_0} \left| \frac{\frac{f(x) - f(x_0)}{f(x_0)}}{\frac{(x - x_0)}{x_0}} \right|</math> | ||
===For a differentiable function of one variable=== | ===For a differentiable function of one variable=== | ||
Revision as of 14:46, 1 May 2014
Definition
For an arbitrary function of one variable
The condition number for a function at a point in the interior of its domain can be defined formally as:
For a differentiable function of one variable
Consider a function of one variable. The condition number of is defined as the absolute value of the relative logarithmic derivative of . Explicitly, the condition number of at a point in the domain of satisfying the conditions that the derivative exists, , and , is defined as:
