ERRATA

Page 18
      Line -4 and Line -6: Change   O(h3)   and   O(h4)   to   O(h2)

Page 67
      Replace   A   by   [A|b]   in Example 2.5.1

Page 22
      Line 6: Change   \eta = 1/3   to   \eta = 21/2     and change   \xi = 3   to   \xi = 11/2

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Page 82
      Scalar Multiplication Box, Line 2: Change   "... denoted by &alphaA, is defined ..."   To   "... denoted by &alphaA (or equivalently A&alpha), is defined ..."

Page 95
      Line 2: Correct the spelling of "introduced"

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Page 107
      Line 12: Change   n   to   k   to make the expression read   Ak = AA...A   (k times)

Page 109
      Lines 2-5, Line 7, and Line 14: For the matrices (but not the vectors) change   P   to   T

Page 121
      Line 6: Make A and B boldface.

Page 129
      Last line before the exercises: Insert a space after "Example 5.12.1"

Page 137
      Line 9: Remove the extraneous period (the first period in the sentence).

Page 139
      Lines 5 and 8: In the subscripts of the displayed equations, enclose   n-r   and   m-r   in parentheses [i.e., write   (n-r)   and   (m-r) ].

Page 155
      The second half of the proof should be rewritten with the roles of R and RT interchanged as follows.
               

Page 169
      Lines -1 and -6: Change the font on R from   \alpha_i\in\cal R   to   \alpha_i\in\Re

Page 173
      Line -11: f should be a function from Rn into Rm (rather than from Rm into Rn)

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Page 176
      Line 10: Delete the transpose superscript on y to make the expression look like this.
             
      Line 16: Change the expression after the last implication to read as follows.
             

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Page 178
      Lines 10 and 12: Add the phrase "(transposed)" to the end of each line.

Page 204
      Line -16: Change     "... m   independent nodal equations."     to     "... m-1   independent nodal equations."

Page 217
      Line 12: Change the matrix in the upper left-hand block to be   ${\bf I}+{\bf E}_{11}$   instead of   ${\bf I}-{\bf E}_{11}$.    

    In other words, the display on line 12 should be $${\bf A}+{\bf E}\sim\pmatrix{{\bf I}+{\bf E}_{11}&{\bf 0}\cr {\bf 0}&{\bf S}\cr}$$

Page 239
      The discussion of the projector in the second bullet does not match Figure 4.7.2. Change the discussion in the second bullet to reference Exercises 3.3.4 and 3.4.1.

Page 239
      Change captions to 8 point font in Figures 4.7.1, 4.7.2, and 4.7.3

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Page 273
      Last line: Change = to less than or equal. Replace the last three lines with the following.

 

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Page 274
      Line 8 below the shaded box: Change the word "integers" to "real numbers"

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Page 278
      Line 9, Exercise 5.1.12b: y should be divided by the q-norm of y rather than x.
                Line 9 should read as follows.
               

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Page 279
      Line 3: The (1,2)-entry in matrix A should be -1 instead of 1.

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Page 281
      Line 6 in the shaded box: Change     to     to read:

           

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Page 283
      Equation (5.2.13): Change   V*V=I   to   VV*=I

Page 285
      Exercise 5.2.6 (e): Change   V*V=I   to   VV*=I

Page 288
      Lines 4 and 5 in the proof: Replace with the following.

 

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Page 289
      Line -4 (in the text): Delete the exponent on ||x||.   i.e., change ||x||2   to  ||x||

Page 291
      Example 5.3.4: The equation in the middle of the page should read as follows.
                 

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Page 297
      Line 9: Change   x and y   to   zx and zy

Page 302
      Line 6: Change   4/n&pi   to   4/(n&pi)

Page 320
      The proof that isometries are unitary is incorrect. Change the proof to read as follows.

           

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Page 328
      Line -3 inside of the shaded box: Add a subscript z to the boldface P to make the line read:

               

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Page 333
      First line below shaded box: Change "...rotations matrices..." to "...rotation matrices..."

Page 354
      Line 15: The formulas for computing the paramaters for a Jacobi rotation are not correct. Replace them with the ones shown below.
               

Page 357
      Last line in shaded box: Make it read as follows.

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Page 364
      Line 3: Change   128/2 = 64   to   512/2 = 256.
      Insert 1/2 in front of the matrix in the equation at the bottom of the page

Page 373
      Line 7 inside of the shaded box: The shape subscript on vector D should be   2 j x1   instead of   j+1x1
      Last line inside of the shaded box: Change to

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Page 379
      Exercise 5.8.12, Line 5: Change   cj-k mod(n)    to    c(j-k) mod(n)

Page 383
      Last line in shaded box: Add the parenthetical phrase (empty set) after greek letter phi

               

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Page 395
      Entire page: The properties and their proofs have been changed to be more precise and more rigorous.

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Page 398
      Example 5.10.3: Line 1 should read as follows.
               

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Page 389
      Figure 5.9.2: Delete the greek subscript gamma from each greek theta

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Page 398
      Example 5.10.3: Line 1 should read as follows.
               

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Page 403
      Line 1 below the first box: Change "... is a single vector ..." to "... is a single nonzero vector ..."

Page 412
      Last Line: Change the subscript   r   to   n

Page 414
      Line 12 (last line in box): Change   "... A is an orthogonal matrix."   to   "... A is a multiple of an orthogonal matrix."

Page 419
      Line -9: Change   qn   to   qm in the query vector   qT

Page 420
      Line 13: Change   sk   to   sn

Page 429
      First line below the shaded box: Remove an extra "illustrated"

Page 435
      Last Line: Change the last term in this line from   ||p-m||22   to   ||b-p||22

Page 442
      Problem 5.13.17 (b): There are missing brackets. The expression should be: p=b-((u^Tb-beta)/uTu)u.

      Problem 5.13.18 (b): The expression should be: p=b-(u^Tb/u^Tw)w.

      Problem 5.13.18 (c): The expression should be: p=b-((u^Tb-beta)/u^Tw)w.

Pages 454-455
      Minor corrections and simplifications are made.

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Page 459
      Paragraph 2, Line 7: Change   Liebniz   to   Leibniz.

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Page 483
      Exercise 6.2.6: Change:     cnx1   to   cmx1

Page 497
      Line 9: Change:   x   to   xT

Page 498
      Line 2: Change:   "... are contained the union ..."   To:   "... are contained in the union ..."

Page 504
      Line 1: Make the subscript on greek xi lower case. The line should read
               

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Page 510
      Line 11: Delete extra space between p. and 590

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Page 521
      Exercise 7.2.7 is incorrectly worded. Replace it as shown below.
               

Page 527
      Example 7.3.1, Line2: Change lower limit of summation in Neumann series expansion from k=1 to k=0

Page 534
      Footnote, last line: Change "(1910-)" to "(1910-2001)"       (Wielandt died on February 14, 2001)

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Page 548
      Line 5: Change   = U =   to   =

Page 549
      Line 6: Add the parenthetical remark   (all quantities in the proof on p. 547 become real when "normal" is replaced by "real-symmetric")   at the end of the first sentence of the second paragraph.

Page 562
      Lines 13, 15, and 19: Change "fundamental mode(s)" to "normal mode(s)"
      Line 16: Reverse the signs in lambda_2 and lambda_3 to read
               

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Page 570
      Line 4: The Hessian term in the display should be divided by 2. The correct formula is

               

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Page 571
      Lines 15 and 27: Change "fundamental mode(s)" to "normal mode(s)"

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Page 574
      Lines 9 and 10: The last sentence of the first paragraph should read
                "... for every singular matrix A of index k with rank(Ak) = r, there is ..."

Page 578
      Lines 9, 10, and 11: Change   X4   to   X4

Page 598
      Line 13, Exercise 7.8.11: Reverse the roles of the exponents   m   and   n
              The correct statement is  

Page 615
      Change Exercise 7.9.22 as follows.
             

Page 627
      Line -3: Change 7.10.28 to 7.10.25

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Page 648
      Remove the "det" in front of (xI - N)-1 in the equation on the middle of the page

Page 659
      Exercise 7.11.4: Change m(x) and c(x) as follows.
              m(x) = (x - λ)(x - μ)2
              c(x) = (x - λ)3(x - μ)3

Pages 663-686
      A complete update to Sections 8.2 & 8.3

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Note: In addition to other minor corrections, this update corrects the following known errors.

Page 685
      Exercise 8.3.7 (b). The corrected solution is as follows.

                 

Page 691
      Line 12: Change (8.3.8) to (8.3.10)
                (Note: Make this change only if you installed the update for Sections 8.2 & 8.3 on pages 663-686.)

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Page 695
      Line 5, equation (8.4.6): Change   Prr   to   P1r   in the first row of matrix   P   in (8.4.6).

Page 697
      Line 12, equation (8.4.8): Change   Prr   to   P1r   in the first row of   T11   in (8.4.8).

INDEX Page 708
      Line 36: Add the entry --- empty set, 383

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INDEX Page 709
      Change "fundamental mode of vibration" to "fundamental (normal) mode of vibration"

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INDEX Page 713
      Insert a new entry into the index -- "normal modes of vibration, 562, 571"

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SOLUTIONS MANUAL Page 25
      Solution 3.10.10 The Cholesky factor is upper triangular, and it is the transpose of the matrix given.

SOLUTIONS MANUAL Page 42
      Solution 4.7.4 The solution is missing. It will be included in the next edition.

SOLUTIONS MANUAL Page 53
      Solution 5.2.1 part c: The answer is 9 instead of sqrt{9}

SOLUTIONS MANUAL Page 54
      Solution 5.2.6 part e: Change   V*V=I   to   VV*=I

SOLUTIONS MANUAL Page 71
      Solution 5.8.2 part b: The answer is e4 instead of 4e4

SOLUTIONS MANUAL Page 73
      Solution 5.8.6 parts b and c: Reverse the order of the components in the vectors on the left side of the equations in (b) and (c)---right side is okay.

SOLUTIONS MANUAL Page 92
      Solution 5.10.12 parts (b) implies (c), (c) implies (d), and (d) implies (e) should read as follows.

               

SOLUTIONS MANUAL Page 102
      Solution 5.12.16 part (d): Replace the first identity matrix I with VT and the second I with V. Also, respectively insert V and VT on the left and right-hand side of D2.

      Solution 5.12.16 part(i): The last term in the second equality should be VT instead of V, and the first term in the third equality should be V instead of VT. Also very last equality should be removed.

SOLUTIONS MANUAL Page 129
      Solution 7.1.22 part b: Make all subscripts on greek xi lower case. The expression should read
               

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SOLUTIONS MANUAL Page 132
      Solution 7.2.6: The constant term in the characteristic equation should be   9/10   instead of   1/2.

SOLUTIONS MANUAL Page 132-133
      Solution 7.2.7: Exercise 7.2.7 has been reworded---see Errata for pg. 521. New solution is given below.
               

SOLUTIONS MANUAL Page 134
      Solution 7.2.14: Last line of display: Change   < alg multA   to   = alg multA

SOLUTIONS MANUAL Page 139
      Solution 7.3.9: Change the last five sentences to read as follows.

               

SOLUTIONS MANUAL Page 146
      Line 1: Change "fundamental modes" to "normal modes"
      Solution to Exercise 7.6.4: Change     18u2 + 8v2 = 72     to     8u2 + 18v2 = 72

SOLUTIONS MANUAL Page 149
      Solution to Exercise 7.7.7, Line 6: Change     dim R(L) = 2 = dim R(L)     to     dim R(L) = 2 = dim N(L)

SOLUTIONS MANUAL Page 154
      Solution to Exercise 7.9.5: Change     f(z) = zn     to     f(z) = zk
      Solution to Exercise 7.9.6: The (3,3)-entry in the matrix   eA  should be   7e4 - e2   (the 7 was missing).

SOLUTIONS MANUAL Page 155
      Solution to Exercise 7.9.9: The answer to the second part of the question is "no." Consider a 2x2 matrix with eigenvalues 1 and -1 along with the function f(x) = x2.

SOLUTIONS MANUAL Page 158
      Solutions to Exercises 7.9.22 and 7.9.23 should be changed as follows.
               

SOLUTIONS MANUAL Page 161
      Solution to Exercise 7.10.9, Line 5: Change     |1+w|n     to     |1-w|n

SOLUTIONS MANUAL Page 165
      Solution to Exercise 7.11.4: The problem has been changed (see above). The solution is changed by removing one μ from the diagonal.

SOLUTIONS MANUAL Pages 167-171
      Solutions to exercises in Chapter 8 have changed.
                Problems have been added and deleted in the revision of sections 8.2 and 8.3.

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Back Cover
      Correct the spelling of Mathematics in SIAM's address.


      Please send other errors that you have discovered or suggest improvements.