### 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)

• (Page x, Line +9)
• (Page xii, Line +6)
Replace Examples of general-purpose mathematical libraries ...''
with References to general-purpose mathematical libraries ...''
• (Page xii, Line -14)
• (Page xii, Line -6 to -5) omit sentence:
"Such sections are marked with an asterisk."
• (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}.
• Page 35, Problem 19: Should read: $x(\lambda)=[\lambda, \lambda^2, \lambda^3, \ldots]$
• Page 127, Caption Figure 3.8
Instead of "... $p(x) = z^5 + 1$" it should read: "...$p(z) = z^5 -1"$
• Page. 128, Line 5
Instead of $p(z) = z^5+1$ should read: $p(z) = z^5-1$
• (Page 190, Line 5)
Replace "from Definition (6)" with "from Equation (6)"
• (Page 203, Line 5)
Replace exponent $m$ with $m+1$ to read: $||I - BA||^{m+1} ||x^{(0)}- x||$
• (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 .."
• (Page 260, Line -10)
add equation number (5) to last displayed equation proof of THEOREM 1.
• (Page 271, Problem 5.2.9)
Remove Hint: Use Gershgorin's Theorem.
• (Page 288, Line +1)
Replace (See Problem 5.3.39, p. 287)'' with (See Problem 5.4.39, p. 298)''
• (Page 331, Solution Example 1, Line -2): Change to read: 5 2 | 2
• (Page 359, Line -4): Change upper limit in summation from m to n to read: $\sum_{j=0}^n b_j t_j^i = 0$
• (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 $i=n-1,n-2,...,1$.
• (Page 450, Problem 4) Should be $f(x_j)=\langle g, E_{-j}\ranlge_n$
• (Page 495, Line +3): Change to : $x^2 - \frac13$
• (Page 498, Problem 7.3.3, Last two displayed lines): Should be x_0 = -x_2 = ... and x_1 = -x_3 = ...
• (Page 510, Equation (10) right-hand side: change 30 to 60
• (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"
• (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."
• (Page 547, Computer Problem 8.3.6, Line 3)
Change $-(2+\sqrt{2})F_2$ to $+(2-\sqrt{2})F_2$
• (Page 548, Computer Problem 8.3.9)
Line -2: Change 891/8329 to 891/8320
Line -1: Change -539/394 to -539/384
• (Page 571, Computer Problem 8.6.3) Change differential equations to read: x'_1 = -13x_1 + 6x_2; x'_2 = -13x_2 - 6x_1
• (Page 602, Equation (15))
Remove extra zero from right hand side vector.
• (Page 617, Line 9)
Add: ... can be used are these from (3) p. 466, (8) p. 468, and (9) p. 469:
• (Page 617, Line 13)
Add: ... affording various degrees of precision. (See problems in Section 7.1.)
• (Page 618, Figure 9.3)
Horizontal axis should be labeled as $g(x)$ not $g(t)$.
• (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."
• (Page 633, Line -9 before Problems 9.3)
Replace $\sinh$ with $\sin$ to read:
$g(x,y)=10^{-4}\sin(3\pi x)\sin(3\pi y)$
• (Page 633, Line -1 above Problems 9.3)
Insert phrase: when programmed in double precision.
• (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.
• (Page 703, Line +6)
Remove transpose in displayed equation $A=AD^T$ to read: $A=AD$
• (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)
• (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)
• (Page 705, Line -2)
Change $D_q$ to $D_3$ to read: $x - \lambda D_3 =$ ...
• (Page 706, Line +2)
Change $D_q$ to $D_3$ and $d_3$ to $e_3$ to read:
$y = x - \lambda D_3+\lambda e_3 = [0\quad 1\quad 1\quad 0\quad 0]^T$
• (Page 711, Section 11.5 title, Line 8)
• (Page 711, Line -10)
Replace "Nocedal-Wright [1999] has written a recent textbook..." with "Nocedal-Wright [1999] is a recent textbook ..."
• (Page 714, Line -12)
For this case, these replacements should be carried out in strict order:
• (Page 714, Line -6)
Insert "in strict order" to read:
The replacement needed are then in strict order:
• (Page 715, Problem 11.1.1, Line 2)
Insert "approximately" to read: ... by a factor of approximately 0.62.
• (Page 721, ALGORITHM 1, Step 1)
Insert "Compute" and replace equal sign ($=$) with left arrow ($\leftarrow$)
• (Page 722, Line 4)
Remove comma before where to read: "...on the ray $x^{(k)}+tv^{(k)}$ where $f$ has ..."
• (Page 722, Section 11.5: title, Line 1)
• (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"
• (Page 723, end of Section 11.5, Line -5, -2)
• (Page 727, Line -6) Change Aubin [2000] to Aubin [1998]
• (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:
$\lambda u_i + \theta v_i > \lambda f_i(x) + \theta f_i(y) \ge f_i(\lambda x + \theta y) = f_i(\omega)$
• (Page 747, add missing reference) Aubin, J. P. 1998. Optima and Equilibria: An Introduction to NonLinear Analysis, 2nd ed. New York: Springer-Verlag
• (Page 761, Line -12)
Nelder, J.A., and R. Mead, 1965. ...
• (Page 778, add to of top second column with overhang of two characters)
Lemma on (continued)
• (Page 780, column 1, Line 5)
• (Page 785, 786, add to of top second column with overhang of two characters)
Theorem on (continued)
• (Page 787, add to top of first column with overhang of two characters)
Theorem on (continued)
• (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); Granville Sewell (sewell@math.utep.edu), Lim Chia Sien (limcs@mail.utar.edu.my); Jim Shapiro (jimshapiro@gmail.com);
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 11/22/2008