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Linear Algebra

Exercise 6.10.4

Answers

1.

Use the previous exercise. We know that

∥ A ∥ = 84.74

and

∥ A^{- 1} ∥ = \frac{1}{0.0588} ≅ 17.01

. And the condition number is the ratio

cond (A) = \frac{84.74}{0.0588} ≅ 1443 .

2.

We have that

∥ \tilde{x} - A^{- 1} b ∥ = ∥ A^{- 1} (b - A \tilde{x}) ∥ \leq ∥ A^{- 1} ∥ ∥ b - A \tilde{x} ∥ = 17.01 \times 0.001 = 0.017

and

\frac{∥ \tilde{x} - A^{- 1} b ∥}{∥ A^{- 1} b ∥} \leq cond (A) \frac{∥ δb ∥}{∥ b ∥} ≅ \frac{14.43}{∥ b ∥}

by Theorem 6.44.

jephianlin

2011-06-27 00:00

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