# 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 $2^n-1$“.