Numerical Analysis:
Mathematics of Scientific Computing, 3rd Edition
David Kincaid & Ward Cheney
Brooks/Cole Publ. Co., 2002, ISBN 0-534-38905-8
Errata List (First and Second Printings)
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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."
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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: $x(\lambda)=[\lambda, \lambda^2, \lambda^3, \ldots]$
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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: $p(z) = z^5-1$
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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 .."
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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)''
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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 $f(x_j)=\langle g, E_{-j}\ranlge_n$
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(Page 495, line +3):
Change to : $x^2 - \frac13$
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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
lines -1:
change "end do" to "end while"
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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 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.
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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.
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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:
$y = x - \lambda D_3+\lambda e_3 = [0\quad 1\quad 1\quad 0\quad 0]^T$
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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:
\[
\lambda u_i + \theta v_i > \lambda f_i(x) + \theta f_i(y) \ge
f_i(\lambda x + \theta y) = f_i(\omega)
\]
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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. ...
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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
Brooks/Cole Publ. Co., 2002, ISBN 0-534-39104-4
Errata List
-
(page 31, Problem 3.1.2b)
Change $c_0$ to $a_0$
Thanks and Acknowledgements for Errata in NA3 to:
Willy Chen (willy_chen81@hotmail.com);
Chris Engels (cengels@engr.uky.edu);
Justin Gottshlich (justin@modeka.com);
Guus Jacobs (Brown Univ.gjacobs2@dam.brown.edu);
Chunqing Lu (So. Illinois at Edwardsville, clu@suye,eduy);
Marc Mehlman (U. New Haven MarcMehlman@yahoo.com);
Keith M. Briggs (Btexact Tech Keith.Briggs@bt.com);
Sadegh Jokar (Sharif Univ. Tehran, s_jokar@math,sharif.edu),
Johan de Klerk;
Oscar Lopez-Pouso (Univ Sandiago de Composadella, Spain oscarlp@usc.es);
Saadet Erbay (serbay@isikun.edu.tr);
Stefan Paszkowski (Wroclaw, Poland, S.Paszkowski@int.pan.wroc.pl);
Niloufer Mackey (nil.mackey@wmich.edu);
Lim Chia Sien (limcs@mail.utar.edu.my);
Jim Shapiro (jimshapiro@gmail.com);