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“.