Condition number

Definition

For an arbitrary function of one variable

The condition number for a function $f$ at a point $x_0$ in the interior of its domain can be defined formally as:

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For a differentiable function of one variable

Consider a function $f$ of one variable. The condition number of $f$ is defined as the absolute value of the relative logarithmic derivative of $f$. Explicitly, the condition number of $f$ at a point $x_0$ in the domain of $f$ satisfying the conditions that the derivative $f^{\prime }(x_0)$ exists, $x_0\ne 0$, and $f(x_0)\ne 0$, is defined as:

$\left|\frac{x_0{f}^{\prime }(x_0)}{f(x_0)}\right|$