Functions of Matrices: Theory and Computation
Errata

Page 3, (1.4): there is an unwanted right parenthesis in the (1,m_k) position.

Page 4, line 6: replace E_k by N_k.

Page 10, second paragraph of Section 1.2.6:
$\psi(t)$ is the minimum polynomial for $n>5$ but not for $n=4$,
because $F_4$ has a repeated eigenvalue 1.

Page 27, line 8: replace "it" by "its".

Page 31, Problem 1.33: the displayed matrix should have an extra
superdiagonal of 1s inserted immediately above the main diagonal, so
that
$$
A =
\left[ \matrix{
1 & 1 & \frac{1}{2!} & \frac{1}{3!} & \dots &
\frac{1}{(n2)!} \cr
& 1 & 1 & \frac{1}{2!} & & \vdots \cr
& & 1 & \ddots & \ddots & \vdots \cr
& & & \ddots & \ddots &\frac{1}{2!} \cr
& & & & \ddots & 1 \cr
& & & & & 1 \cr
}\right]
$$.

Page 80, line 1: should read "[0/0], [1/1], [2/2], ...".

Page 86: In lines 1 and 2 of Algorithm 4.14, n should be m, where T is
block mbym.

Page 97, last displayed equation should read
$$
\norm{E_k} \le c \norm{E_0} + c \norm{E_{k1}}
c \sum_{i=1}^{k1} o( \norm{E_{k1i}} )
\le c \norm{E_0} + (1+(k1)c) \cdot o( \norm{E_0} ).
$$

Page 102:
in (4.37), and three lines below it,
$f(\rho(A))$ should be replaced by $\max_i f(\lambda_i)$.

Page 114, line 6: remove the period inside parentheses and replace "It" by
"it" on the following line.

Page 120, line 5: should read "the $\lambda_i$ are".

Page 160, line 14 should read "if $A$ is a nonsingular $M$matrix
with $0< a_{ii} \le 1$ for all $i$ then all the iterates $X_k$
(or $Z_k$ in the case of iteration (6.19)) have the same properties.

Page 165, line 3: $u_{ij} = {ni+1 \choose nj+1}$ should read
$u_{ij} = {ni \choose nj}$.

Page 161, Theorem 6.10 should say "A\in\mathbb{R}^{n\times n}"
and the sentence before the theorem should say "real $H$matrices".

Page 217, line 3: the parentheses should read ("Berberian's trick").

Page 224, line 9 of Algorithm 9.4 should read \omega_{s+1+r}
and on line 10 add, just before "quit", "F = F_s".

Page 222, line 9: $M^n=0$ should read $N^n=0$.

Page 228, in line 6 of Algorithm 9.6 i should be j;
in line 8 of Algorithm 9.6 j should be i.

Page 234, Table 10.1: formula in (3,2) position should read
$Q e^T Q^*$.

Page 246, line 7: the first right parenthesis after $I$ should be deleted.

Page 247, third line above Theorem 10.21: "scaling" should read "squaring".

Page 253, line 2: "larger" should read "smaller".

Page 261, in the first line of Section 10.7.3 a space is needed after "single shift".

Page 265, Problem 10.6 should read "cond_abs(exp,A)".

Page 266, Problem 10.16 should read "rounding errors in the squaring phase".

Page 272, second display from bottom:
on lefthand side, $\kappa_{\log}(A)$ should read $\mathrm{cond}_{\mathrm{rel}(\log,A)$.

Page 274, line 8 should read "$m$point GaussLegendre quadrature rule"

Page 275, line 10: extra right parenthesis needed before the final
"".

Page 280, line 1: the U should be in the mathcal font.

Page 280: in (11.28), the conditions for the second case should be replaced
by
$z > \frac{1}{\delta} \text{or} z+1 < \delta \text{or} z1 < \delta$
for some suitable $\delta$ that depends on the unit roundoff.

Page 283, line 11 of Algorithm 11.12: $L = 2G_0$ should read $L = 2G_1$.

Page 283, 7 lines before Section 11.9: should read "Algorithm 11.2 can
be combined".

Page 330, line 5: should read "on Hermitian matrices".

Page 332, 9 lines before Section B.16: should read "a complex addition
requires 2 real additions".

Page 333, in equation (B.25) a right parenthesis should be added after
$x_{j1}$.

Page 336:

delete the "LU" line (appears in Table C.2).

HM line should read "$2n^3$".

TY = B line should read "$n^3/3$".

HY = B line should read "$5n^3/3$".

Page 370, in solution to Problem
8.26, in (b) the operation count for (8.37) should be
$3mn^2 + n^3/3$.