Numerical Analysis:
Mathematics of Scientific Computing, 3rd Edition
David Kincaid & Ward Cheney
Errata List
PREFACE
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Dedicated, in memoriam, to our parents
Sarah and Robert B. Kincaid, and Carleton Elliot Cheney.
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(Page x, Line +9)
Change "Meade" to 'Mead" to read:
11.5 Nelder-Mead Algorithm
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(Page xii, Line +6)
Replace ``Examples of general-purpose mathematical libraries ...''
with
``References to general-purpose mathematical libraries ...''
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(Page xii, Line -14)
Change "Meade" to 'Mead" to read:
Nelder-Mead algorithm, ...
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(Page xii, Line -6 to -5) omit sentence:
"Such sections are marked with an asterisk."
CHAPTER 1
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(Page 16, Lines 14-27)
An example of a sequence that converges to $\sqrt{2}$ is
\[ x_{n+1} = x_n - (x_n^2 - 2)[\frac{x_n - x_{n-1}}{x_n^2 - x_{n-1}^2} \]
Selecting two initial values, we have
\[\eqalign{x_1 &= 2\cr
x_2 & 1.5\cr
x_3 &= 1.42857\,1\cr
x_4 &= 1.41463\,4\cr
x_5 &= 1.41421\,6\cr
x_6 &= 1.41421\,4 \]
The convergence to $\sqrt{2}=1.41421\,3562\ldots$ is quite rapid.
Using double-precision computations, we find numerical evidence that
\[ \frac{|x_{n+1} - \sqrt{2}|}{|x_n - \sqrt{2}|^1.62}\le 0.77 \]
which corresponds to {\bf superLinear convergence}.
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Page 35, Problem 19:
Should read: $x(\lambda)=[\lambda, \lambda^2, \lambda^3, \ldots]$
CHAPTER 3
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Page 127, Caption Figure 3.8
Instead of "... $p(x) = z^5 + 1$"
it should read: "...$p(z) = z^5 -1"$
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Page. 128, Line 5
Instead of $p(z) = z^5+1$ should read: $p(z) = z^5-1$
CHAPTER 4
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(Page 190, Line 5)
Replace "from Definition (6)" with "from Equation (6)"
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(Page 203, Line 5)
Replace exponent $m$ with $m+1$ to read:
$||I - BA||^{m+1} ||x^{(0)}- x||$
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(Page 215, Theorem 5, Line 3,5)
Replace "For the iteration formula" with "In order that the iteration formula"
Replace "to produce a sequence" with "produce a sequence .."
CHAPTER 5
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(Page 260, Line -10)
add equation number (5) to last displayed equation proof of THEOREM 1.
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(Page 271, Problem 5.2.9)
Remove Hint: Use Gershgorin's Theorem.
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(Page 288, Line +1)
Replace
``(See Problem 5.3.39, p. 287)''
with
``(See Problem 5.4.39, p. 298)''
CHAPTER 6
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(Page 331, Solution Example 1, Line -2):
Change to read: 5 2 | 2
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(Page 359, Line -4):
Change upper limit in summation from m to n to read:
$\sum_{j=0}^n b_j t_j^i = 0$
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(Page 361, Problem 6.4.1:
Refer to the tridiagonal algorithm for determining the values of $z_i$.
Prove that $u_i z_i + h_i z_{i+1} - v_i = 0$ for all $i=n-1,n-2,...,1$.
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(Page 450, Problem 4)
Should be $f(x_j)=\langle g, E_{-j}\ranlge_n$
CHAPTER 7
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(Page 495, Line +3):
Change to : $x^2 - \frac13$
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(Page 498, Problem 7.3.3, Last two displayed lines):
Should be x_0 = -x_2 = ...
and x_1 = -x_3 = ...
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(Page 510, Equation (10)
right-hand side: change 30 to 60
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(Page 511, pseudo-code)
Line -12, right-hand side: change 30 to 60
Lines -5 to -2:
move indentation left four spaces
Line -3:
Third vector component should be $v_4^{(k-1)}$ not $v_5^{(k-1)}$
Lines -1:
change "end do" to "end while"
CHAPTER 8
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(Page 525, Line 4 after (3))
Replace "we can expect that at some finite value of t there will be no
solution; that is, $x(t)=+\infty$."
with "we should be prepared for a solution that has a
vertical asymptote."
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(Page 54, Problem 8.3.6, Line 1)
Change "order 4" to "order 5"
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(Page 547, Computer Problem 8.3.6, Line 3)
Change $-(2+\sqrt{2})F_2$ to $+(2-\sqrt{2})F_2$
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(Page 548, Computer Problem 8.3.9)
Line -2:
Change 891/8329 to 891/8320
Line -1:
Change -539/394 to -539/384
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(Page 571, Computer Problem 8.6.3)
Change differential equations to read:
x'_1 = -13x_1 + 6x_2; x'_2 = -13x_2 - 6x_1
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(Page 602, Equation (15))
Remove extra zero from right hand side vector.
CHAPTER 9
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(Page 617, Line 9)
Add:
... can be used are these from (3) p. 466, (8) p. 468, and (9) p. 469:
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(Page 617, Line 13)
Add:
... affording various degrees of precision. (See problems in Section 7.1.)
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(Page 618, Figure 9.3)
Horizontal axis should be labeled as $g(x)$ not $g(t)$.
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(Page 619, Line 7)
Replace sentence:
"An analysis following the algorithm will show why this is true."
with
"An analysis in the following paragraphs will show why this is true."
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(Page 633, Line -9 before Problems 9.3)
Replace $\sinh$ with $\sin$ to read:
\[ g(x,y)=10^{-4}\sin(3\pi x)\sin(3\pi y)\]
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(Page 633, Line -1 above Problems 9.3)
Insert phrase: when programmed in double precision.
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(Page 642, restate problem 4)
Prove that if the Dirichlet problem defined by Equations (7) and (8)
has a solution, then it has a solution that satisfies the symmetry
conditions of Problem 3.
CHAPTER 10
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(Page 703, Line +6)
Remove transpose in displayed equation $A=AD^T$ to read: $A=AD$
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(Page 703, Lines -10,-4,-3,-1)
Change $d_q$ to $e_q$ to read:
where $y=x-\lambda D_q - \lambda e_q$ (Line -10)
$=c^Tx+\lambda(c_q-e_q)$ (Line -4)
.. we shall select $q$ so that $c_q>e_q.$... (Line -3)
to select $q$ so that $c_q-e_q$ is as large as possible. ... (Line -1)
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(Page 705, Line +2, +3)
Remove transpose on $D^T$ (3 times) to reads:
... Then $Ax=b=Au=A(Du).$
It follows that $x=Du$ because $Ax$ (twice in Line 2 )
and $ADu$ are Linear combinations ... (Line 3)
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(Page 705, Line -2)
Change $D_q$ to $D_3$ to read:
$x - \lambda D_3 = $ ...
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(Page 706, Line +2)
Change $D_q$ to $D_3$ and $d_3$ to $e_3$ to read:
$y = x - \lambda D_3+\lambda e_3 = [0\quad 1\quad 1\quad 0\quad 0]^T$
CHAPTER 11
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(Page 711, Section 11.5 title, Line 8)
Change "Meade" to 'Mead" to read:
11.5 Nelder-Mead Algorithm
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(Page 711, Line -10)
Replace "Nocedal-Wright [1999] has written a recent textbook..."
with "Nocedal-Wright [1999] is a recent textbook ..."
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(Page 714, Line -12)
Insert "strict" to read:
For this case, these replacements should be carried out in strict order:
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(Page 714, Line -6)
Insert "in strict order" to read:
The replacement needed are then in strict order:
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(Page 715, Problem 11.1.1, Line 2)
Insert "approximately" to read:
... by a factor of approximately 0.62.
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(Page 721, ALGORITHM 1, Step 1)
Insert "Compute" and replace equal sign ($=$) with left arrow ($\leftarrow$)
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(Page 722, Line 4)
Remove comma before where to read:
"...on the ray $x^{(k)}+tv^{(k)}$ where $f$ has ..."
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(Page 722, Section 11.5: title, Line 1)
Change "Meade" to 'Mead" to read:
Nelder-Mead Algorithm (twice)
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(Page 723, Line 16)
Replace "the relative \textbf{flatness} is small, which is the quantity"
with "the relative \textbf{flatness} is small.
This is defined to be the quantity"
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(Page 723, end of Section 11.5, Line -5, -2)
Change "Meade" to 'Mead" to read:
Nelder and Mead (twice)
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(Page 727, Line -6) Change Aubin [2000] to Aubin [1998]
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(Page 728, Line 10)
At beginning of displayed equation change $\lambda_i u$ to
$\lambda u_i$ and add $=f_i(\omega)$ to the end to read:
\[
\lambda u_i + \theta v_i > \lambda f_i(x) + \theta f_i(y) \ge
f_i(\lambda x + \theta y) = f_i(\omega)
\]
BIBLIOGRAPHY
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(Page 747, add missing reference)
Aubin, J. P. 1998. Optima and Equilibria: An Introduction to NonLinear
Analysis, 2nd ed. New York: Springer-Verlag
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(Page 761, Line -12)
Change "Meade" to 'Mead" to read:
Nelder, J.A., and R. Mead, 1965. ...
INDEX
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(Page 778, add to of top second column with overhang of two characters)
Lemma on (continued)
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(Page 780, column 1, Line 5)
Change "Meade" to 'Mead" to read:
Nelder-Mead algorithm, 722
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(Page 785, 786, add to of top second column with overhang of two characters)
Theorem on (continued)
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(Page 787, add to top of first column with overhang of two characters)
Theorem on (continued)
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(Page 787, add to second column, after line 9)
Traveling salesman problem, 724-725
Instructor's Solution Manual for Numerical Analysis:
Mathematics of Scientific Computing, 3rd Edition
David Kincaid & Ward Cheney
Errata List
-
(Problem 2.1.7)
Should read:
Thus, there are
$2\cdot 2^{23}(2^8 - 2) = 2^{25}(2^7 -1) =2^{25}(127) = 4,261,412,864
different numbers.
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(Problem 2.2.3)
Insert at beginning to solution:
No. For example, consider the case $x = 5$.
Add to end of Hint:
See Abramowitz-Stegun Handbook online at
{\tt www.math.ucla.edu/~cbm/aands/} or doing a Google search for it.
-
(Problems 2.2.4 \& 2.2.5)
Interchange solutions to Pbs 2.2.4 and 2.2.5.
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(Problem 3.1.2b)
Should read
$| r - c_n | \le 2^{-(n+1)} (b_0 - a_0) = 2^{n}$
Thanks and Acknowledgements:
Keith M. Briggs,
Willy Chen,
Chris Engels,
Saadet Erbaym,
Magdy Girgis,
Justin Gottshlich,
Li Hang,
Guus Jacobs,
Sadegh Jokar,
Chunqing Lu,
Marc Mehlman,
Saulo Oliveira,
Johan de Klerk,
Oscar Lopez-Pouso,
Niloufer Mackey,
Stefan Paszkowski,
Granville Sewell,
Jim Shapiro,
Lim Chia Sien,
Jim Shapiro,