Abstract :
Classically, the relative error in as an approximation to α is measured by . The quantity −log10δ is usually used for the number of correct decimal digits in numerical results, although this δ-measure is clearly not a metric, since it lacks symmetry between α and ga. In part I of this series, two other kinds of relative distances which have much better mathematical properties have been introduced and employed to establish theories. It is shown that these different measurements are topologically equivalent. However, the δ-measure is more convenient to use in practice. In this part, we established relative perturbation bounds directly using the classical measure. The new bounds for diagonalizable matrices are cleaner than the corresponding ones in part I and yield nice bounds for Hermitian matrices, too. But when applied to nonnegative definite Hermitian matrices, the new bounds are weaker than those in part I.
