Errata for Accuracy and Stability of Numerical Algorithms, Second edition

In the list below, line numbers do not include tables.

First Printing

Page 198, line -3: change $|\widehat{r}_i^T \widehat{r}_j|$ to $|\widehat{r}_i^T| |\widehat{r}_j|$ .
Page 517, Theorem 28.1 should read as follows:
Let the independent vectors $x_i \in \mathbb{R}^{n-i+1}$ have elements from the normal $N(0,1)$ distribution for $i=1\colon n$ . Let $P_i = \mathrm{diag}(I_{i-1}, \overline{P}_i)$ , where $\overline{P}_i$ is the Householder transformation that reduces $x_i$ to $r_{ii}e_1$ , for $i=1\colon n-1$ . Then the product $Q = D P_1 P_2 \dots P_{n-1}$ is a random orthogonal matrix from the Haar distribution, where $D = \mathrm{diag}(\mathrm{sign}(r_{ii}))$ and $r_{nn} = \mathrm{sign}(x_n)$ .
Page 519, line -5: the MATLAB statement “charpoly(P)” is not valid in current versions of MATLAB and should be replaced by “poly(sym(P))”.
Page 585, in the second table “mmsmax” should be “nmsmax”.
Page 499, first line of Section 27.8: replace “it estimated” by “is estimated”.

Second Printing

On page 102, in the displayed equations $P_1(x)$ should read $P_1(X)$ and $P_3(x)$ should read $P_3(X)$ .
Page 106, line -4 should read “ $\overline{x}_i y_i$ lies on the same ray”.
On page 123, in (7.10) and several other places “ $|E|x|$ ” should be “ $E|x|$ “.
On page 123, two lines before (7.13) $f = |b|$ should read $f = 0$ .
On page 121, in Theorem 7.5 the definition of $D_R$ should be $D_R := \mathrm{diag}( \|A(i,:)\|_{p/(p-1)})^{-1}$ , that is, the $p$ -norm should be replaced by the $p/(p-1)$ -norm.
On page 127, in the last line of Theorem 7.8 there is a missing x: the parenthesized equation should read $|A||A^{-1}|x = \rho(|A||A^{-1}|) x$ .
On page 128, the second displayed equation should begin $\rho_0(A) =$ .
The curve for complete pivoting in Figure 9.2 on page 169 is incorrect. It should grow more rapidly and reach about $10^6$ at the right-hand end point.
Page 143, line 6: should read $\mathrm{cond}(U(\alpha), e) = \mathrm{cond}(U(\alpha)) \sim 2(1+\alpha)^{n-1}$ as $\alpha \to \infty$ .
On page 148, the 7th line of Algorithm 8.13 should read $y_i = s/|u_{ii}|$ .
On page 168, line 7 should read “Note that $\theta$ satisfies $\kappa_{\infty}(A)^{-1} \le \theta \le n^2 \kappa_{\infty}(A)^{-1}$ .”
On page 177, line -11 should read “p. 193]”.
On page 223, in (11.15) the expression for x should read $x = P^Tw$ .
On page 360, line -3 $n$ should be $m$ and this carries though into the two following $\sqrt{n}$ changing to $\sqrt{m}$ .
On page 522, line -10 the minus sign in the expression following after “ $(i,j)$ element” should be removed.
On page 554, in solution to 10.8 “there are $2^{n-1}$ ” should read “there are $2^n-1$ “.