Exercise 6.10.9

Answers

Since we have $Aδx = δb$ and $x = A^{- 1} b$ , we have the inequalities

∥ δx ∥ \geq \frac{∥ δb ∥}{∥ A ∥}

and

∥ x ∥ \leq ∥ A^{- 1} ∥ ∥ b ∥ .

Hence we get the inequality

\frac{∥ δx ∥}{∥ x ∥} \geq \frac{∥ δb ∥}{∥ A ∥} \frac{1}{∥ A^{- 1} ∥ ∥ b ∥} = \frac{1}{∥ A ∥ \cdot ∥ A^{- 1} ∥} \frac{∥ δb ∥}{∥ b ∥} .

jephianlin

2011-06-27 00:00