Sammanfattning

Relative forward (solution) error:

\begin{displaymath} \frac{\lvert\lvert x - x_{\text{approx}} \rvert\rvert_\infty}{\lvert\lvert x \rvert\rvert_\infty} \end{displaymath}

Relative backward (residual) error:

\begin{displaymath} \frac{\lvert\lvert r \rvert\rvert_\infty}{\lvert\lvert b \rvert\rvert_\infty} \end{displaymath}

The matrix norm of an n x n matrix A is defined as

\begin{equation} \left|\left| A \right|\right|_\infty = \text{maximum absolute row sum} . \end{equation}

The condition number of the n x n matrix A is

\begin{equation} \text{cond}(A) = \left|\left|A\right|\right| \cdot \left|\left|A^{-1}\right|\right| . \end{equation}

Ref: Sauer, p. 88.