Applied Linear Algebra and Numerical Analysis

Errata for the text book (Recktenwald)

Some errors are listed on the author's errata sheets but there are others. This is a list of some we have found this quarter.

Note: Some of these have been corrected in later printings of the book, so they may or may not appear in your copy.

• In problem 15 of Chapter 2, it should say 'fliplr' not 'fliprl'

• page 36: about half way down, there's an extra = sign. It should be:
    >> x = ...
    >> x(end-3, end) = [ ]
  

• Page 253, Section 6.2.1: Another condition is needed to guarantee convergence. In addition to the displayed equation, we must assume that the value of g(x) lies in the interval [a,b] for every x in [a,b].

• Page 257, first displayed equation should have a minus sign: n = - log(...).

• Page 262, equation (6.12) and above, should use the indices k and k-1 instead of k+1 and k to be consistent with the algorithm description.

• Page 285, problem 7, should read |g'(x)| < 1.

• Page 286, problem 14, should read |f(x)| < 5 x 10^{-10}.

• Page 358, problem 7(b) of Chapter 7, it should say B = AD.

• Page 407, second "Rule of Thumb" does not hold for any variant of Gaussian elimination, but is generally approximately true when pivoting is used.

• page 411, the third displayed formula is Ux = b; this should be Ux = y.

• page 449, problem 23. Note that not every choice of three points defines a unique plane of the form specified in this problem. If the matrix is singular then there may be no plane of this form or there could be infinitely many (if the three points lie on a line, then any plane through this line works).

• page 476, displayed equation y_f = A_f x_f should be y_f = A_f c.

• page 528, equation (10.4), the second term in the polynomial should have exponent n-2. In equation (10.6) the (3,1) entry of the matrix should be 4.

• page 529, Example 10.4, in the table the price for 1986 should presumably be 133.5 (rather than 113.5) to match the values in the matlab statements on pages 530 and 531.

• page 533, last displayed equation, the coefficient of L_3(x) should be y_3 rather than y_2.

• page 540 -- see the author's errata for the line where f[x_1,x_2,x_3] is defined. The denominator in this expression should be x_3 - x_1 rather than x_3 - x_2.

• page 538, the first displayed equation. The last term should be
    c_{n+1} (x-x_1) (x-x_2) ... (x-x_n)
  It should end with the (x-x_n) term.

• page 545, in the two displayed equations following the line "The fourth and fifth columns are filled in with", the denominators have the terms in the wrong order. They should be V_{i} - V_{i-2} and V_{i} - V_{i-3} respectively. Also, the divided differences in the numerators have the arguments in the opposite order of the standard notation, though by Property 5 on page 543 these are mathematically correct.

• pages 562-3, equations (10.35) and (10.36): P_i(x) should be P_i(\hat x).

• page 583, the curves in Figure 10.19 are mislabelled. The solid line is the function x*exp(-x) and the dashed line is the spline.

• page 599, Example 11.1: the formulas for the perimeter of the ellipse have two errors:
  L = 4aE   should read   L = (a/2) E
  k = 1-b^2/a^2   should read   k^2 = 1-b^2/a^2

• page 613, equation (11.9), the three 1/h^2 coefficients are wrong. They should be 1/(2h^2), -1/h^2, and 1/(2h^2) respectively.

• page 649, line after (11.42) should read
  "the value of S_2 can be accepted..." (Not S_1, which has an error about 16 times larger than S_2 by (11.40)).

• page 688, equation (12.14), f(t,y) should be f(t, z_j).