Scientific Computing: An Introductory Survey

Engineering at Illinois Engineering at Illinois

Errata

Please report any additional errata not already listed here to author at the following email address: heath@illinois.edu

First Nine Printings

The following errata appear in the first nine printings. To determine the printing number, see the first digit of the “keyline” on the copyright page. The most recent printing has the following keyline: 9 0 QFR/QFR 0

page 48: In Computer Problem 1.17, single precision case should use n = 25 rather than 225.

page 62: Second displayed equation should end with a period rather than a comma.

page 77: In Example 2.17, second entry of right-hand-side vector after elimination should be −0.0001 rather than 0.0001, and computed solution and residual norm change accordingly to [0.6391, −0.5] and 7.04 x 10^(−5), respectively. The point of the example remains valid.

page 103: In Computer Problem 2.17, components of right-hand-side vector should be bi = 1 ⁄ n4 in order for resulting deflections to scale properly with n.

page 133: Zero vector in lower left hand corner of right most matrix in first displayed equation is a row vector, so should have superscript T for transpose.

page 148: In part (h) of Review Question 3.24, “number 1” should read “number is 1”.

page 273: Formula for successive parabolic interpolation should correctly (and less confusingly) be written as v − p/q, where p and q should not have ± signs.

page 282: In last line, B1(2,2) should be 4.667 rather than 0.667.

page 290: In third displayed equation, second minus should be plus, i.e., (w − BYu) should read (w + BYu).

page 340: In first line following second displayed equation, ξ should read ξi.

page 361: First 2 in first line should be deleted, i.e., correct value of integral is simply sqrt(2π).

page 371: In line just prior to last displayed equation, “q = 4” should read “p = 4”.

page 509: In Computer Problem 12.4 (a), doubled word “other other” should read just “other”.

page 541: Date of reference [301] should be 1988 rather than 1990.

First Four Printings

The following errata appear only in the first four printings, and have been corrected in the fifth and subsequent printings. To determine the printing number, see the first digit of the “keyline” on the copyright page.

page 20: Bound on relative error given in first inequality is assuming that x is within the normalized range of the floating-point system.

page 60: Derivation in bottom half of page is oversimplified, and conclusion should be expressed as a first-order bound in t. For specific corrections, see subsequent printings.

page 76: To be rigorously correct, second inequality should have an additional factor of n on right-hand side. This bound is extremely pessimistic in practice, however, and third inequality remains valid as is.

page 86: In Algorithm 2.7, last (innermost) for loop should read “for i = j to n”.

page 98: In Exercise 2.28, numeral “1” in Woodbury formula should be identity matrix “I ” instead.

page 99: Page header should read “Exercises”.

page 134: Near bottom of page, Q1(5,2) should be −0.2041 rather than 0.2041.

page 175: Values of α1 and α2 should both be ½ rather than 1.

page 181: In next to last line, “simultaneous interation” should read “orthogonal iteration”.

page 183: In fourth line above Example 4.15, “orthogonal eigenvectors given by” should read “eigenvectors obtained from”.

page 195: Both entries 0.005 in last matrix should be negative.

page 207: Page header should read “Review Questions”.

page 207: Review Questions 4.57 and 4.58 should be parts (a) and (b) of a single question instead of two separate questions.

page 208: In Exercise 4.7 (a), AH should read AT and in Exercise 4.7 (b), “eigenvectors” should read “eigenvalues”.

page 229: In the second displayed equation, the norms should instead be absolute values, and there should also be absolute values around the right-hand side.

page 237: In second bullet of Section 5.6, “Exercise 9.10” should read “Computer Problem 9.10”.

page 249: In Exercise 5.7, “0.75” should read “1.5”.

page 271: In fifth line above Algorithm 6.1, “1+√5/2” should read “(1+√5)/2” to avoid ambiguity.

page 276: In description of Nelder-Mead algorithm, “centroid of all the points” should read “centroid of the other points”.

page 292: In line immediately preceding first displayed equation, “effect off” should read “effect of”.

page 301: In Exercise 6.6, “Determined” should read “Determine”.

page 302: In Exercise 6.12, “f (y) < f (y)” should read “f (y) < f (x)”.

page 303: In Computer Problem 6.2, insert left parenthesis before 1 in second part of definition of  f (x).

page 323: In line 8 from bottom, for an arbitrary function polynomial interpolation at Chebyshev points minimizes error only approximately, i.e., within a small constant factor.

page 343: In line 12, “can then used” should read “can then be used”.

page 354: In line 14 from bottom, degree of Patterson quadrature rule should read “6n+4” rather than “6n+5”.

page 368: In line 7, “highest” should read “higher”.

page 375: Page header should read “Review Questions”.

page 377: Page header should read “Exercises”.

page 387: Existence result cited near bottom of page requires continuity in t as well as Lipschitz continuity in y.

page 391: In second paragraph of Section 9.3.1, “it is seldom be used” should read “it is seldom used”.

page 397: In final paragraph, Mean Value Theorem is incorrectly applied in this context. Correction is to average over line segment by integrating Jacobian matrix with respect to α over interval [0,1].

page 406: In third displayed equation, insert “h” before k1 in equation for k2, as in first displayed equation on same page.

page 408: The second (implicit) method derived in Example 9.13 is a one-step method, rather than a two-step method. Also, the subscripts for the last two occurrences of β should be 0 and 1 rather than 1 and 2.

page 419: Computer Problem 9.5, “system ODEs” should read “system of ODEs”.

page 429: Example 10.6 is correct, but is unnecessarily difficult to follow because step size h = 0.5 is absorbed into ki values rather than being factored out as in Section 9.3.6. For correction, see accompanying lecture notes or later printings.

page 435: In second line after figure, “produce” should read “produced”.

page 438: Middle of page, in sentence beginning “Assuming the basis functions …” homogeneous boundary conditions should be at a and b rather than 0 and 1.

page 445: In Computer Problem 10.5, values specified for first two components of y (i.e., y1 and y2) at each endpoint are only boundary conditions that should be imposed. Values specified for other two components of y (i.e., y3 and y4), should be taken merely as reasonable starting guesses for “missing” conditions needed for some solution methods, with true values for y3 and y4 at endpoints being determined by final computed solution.

page 468: In first sentence of Section 11.5.1, “equation x = G x + c should read “function g(x) = G x + c.

First Printing

The following errata appear only in the first printing, and have been corrected in the second and subsequent printings. To determine the printing number, see the first digit of the “keyline” on the copyright page.

page 35: Near end of first complete paragraph, in sentence beginning “If MATLAB is not available” delete “are” and comma after “Web”.

page 40: Review Question 1.11 should read “True or false” not “True of false”.

page 62: In fourth line after first displayed equation, doubled word “the the” should read just “the”.

page 102: Computer Problem 2.7 should cite Section 2.4.5 instead of Section 2.3.5.

page 115: In fourth line after first set of displayed equations, “residual small” should read “residual is small”.

page 135: First displayed equation, in middle of page, should end with a period rather than a comma.

page 151: Exercise 3.23 should cite Section 3.4.1 instead of Section 3.2.1.

page 154: Computer Problem 3.7 should cite Section 3.6 instead of Section 3.6.1.

page 166: First cross-reference in last paragraph should cite Section 4.2.2 instead of Section 4.2.1.

page 189: First cross-reference should cite Section 4.2.1 instead of Section 4.3.

page 189: Just below middle of page, “Equating the jth column on each side” should read “Equating the kth columns on each side”.

page 190: The best approximation property of Ritz values and Ritz vectors stated in middle of page does not necessarily hold if matrix is not Hermitian.

page 211: In Computer Problem 4.6, “first two computer exercises” should read “Computer Problems 4.2 and 4.3”.

page 225: In line six, “normally the case” should read “normally be the case”.

page 323: In first displayed equation, “x” should be replaced by “t ”.

page 323: In third line after Fig. 7.5, doubled word “the the” should read just “the”.

page 339: In second sentence, “the calculation” should read “calculating”.

page 341: In first sentence of Section 8.2, “which is a set containing no open subinterval” is not (nor was it intended to be) the definition of a set of measure zero, but is merely a fact about such a set. To avoid any confusion, phrase in question should be replaced by “which is a set that can be contained in the union of a countable number of open intervals of arbitrarily small total length” which is the definition of a set of measure zero.

page 354: In fifth line of next to last paragraph, doubled word “for for” should read just “for”.

page 372: In Table 8.1, second MATLAB function for one-dimensional quadrature should read “quadl” not “quad1” (quad-ell, not quad-one).

page 374: In Review Question 8.24, “meant” should read “mean”.

page 379: In Computer Problem 8.7, “area an ellipsoid” should read “area of an ellipsoid”.

page 405: In second line after first displayed equation, doubled word “the the” should read just “the”.

page 422: In second line of Example 10.1, doubled word “the the” should read just “the”.

page 442: In first line of Section 10.9, doubled word “the the” should read just “the”.

page 474: In third line after Algorithm 11.2, “preconditioners of have” should read “preconditioners have”.

page 496: In caption of Figure 12.1, a minus sign should precede exponent of exponential function.

Additional minor typesetting glitches in punctuation or font occurred in the first four printings on the following pages:

11, 16, 51, 55, 56, 97, 98, 101, 104, 143, 150, 152, 169, 182, 208, 209, 249, 265, 305, 306, 318, 375, 421, 465, 489, 493

These have been corrected in subsequent printings, along with other minor polishing.

Please report any additional errata not already listed here to author at the following email address: heath@illinois.edu