Errata for Parameter Estimation and Inverse Problems, Second Edition

Errata for first printing of 

Parameter Estimation and Inverse Problems, 2nd Edition

Last Updated February 22, 2017.

On page 285 in Equation A.11 the second Equation is supposed to be               x_2 + x_3 = 0 rather than x_1 + x_3 =0.

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On Page 162, just before Equation 6.94

Specifically, to solve for the kth product $\by = \bR_m$…

Should be

Specifically, to solve for the kth product $\by = \bR_m \bv_k$..

(the vector v_k) is missing.

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In Exercise 6.2:

Implement the Landweber iteration and apply it to the Shaw problem from Example 4.3.

Should read

…from Example 3.3

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In Exercise 6.3b, Equation 6.99:

The x should be bold.

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In Exercise 6.3c, Equation 6.102 should be:

\rho_k = \sqrt{ \| x_k \|_2}

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In Exercise 6.6:

“n x n” should be “n by n”…

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Exercise 7.4 should read:

Returning to the problem from Example 5.1 and Exercise 5.1, solve for the density profile of the Earth using total variation regularization.  How does your optimal solution compare to that obtained in Exercise 5.1?

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In Exercise 8.4 (a):

Approximately what water level do you believe is best for this data set? Why

Should read

Approximately what value of $\alpha$ do you believe is best for this data set? Why?

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In Exercise 8.4b:

Delete the self-referential See… sentence in part (b) (bold below):

(b) Perform second-order ( p = 2), frequency-domain Tikhonov deconvolution to

solve this problem. See Exercise 8.4(b).

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On p. 269, Equation 11.37 is missing a leading parenthesis (after “min”).

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Figures 3.11, 3.13, 3.14, 3.15 in Example 3.2 (pp. 78-80) are missing a square on their y-axis labels( they should all read “Acceleration (m/s^2)” ).

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On page 120, in Theorem 4.1, it should be noted that the theorem also requires that 0<= alpha <= 1. In practice we can always rescale G and d to move alpha into this range.

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On page 66, in the line between Equations 3.87 and 3.88, V_.,1 should be U_.,1

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On page 116, in the line below Equation 4.69 in right hand side of second Equation , the “~dk” should not be bold.

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On page 135, the second line below Equation 5.39 should read “Combining (5.38) and (5.39) gives”

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On page 62, in (3.58), the V_.,i terms in the numerator should each have a bold V.

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On page 220, in the second paragraph of Section 9.3, the first sentence should read “constrained by an m-length data vector, …”

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On page 76, it is stated that example problem 3.2 is mildly ill-posed. It would be more accurate to state that it is “moderately” ill-posed. Plotting log(s(i)) vs. log(i) shows a slope of about -2 (alpha=+2), indicating that the problem is indeed moderately ill-posed.

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On page 76, Equation 3.102 should have g(t – \tau) rather than g(\tau – t) in the integrand.

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On page 257, in Equation 11.8, d_n should be d_m.

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On page 38, in Equation 2.58, in the third line, there should be a transpose on the last m_L2 on that line.

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On page 238, in the text preceding Equation 2.59, G_2^T should be G_w^T.

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On page 244, where Equation 10.9 defines the Jacobian, the lower part the second term (upper right of the matrix) is missing its partial derivative sign.

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On page 145, Example 6.1 refers to Exercise 4.4, but should refer to Exercise 3.4.

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On page 106, in Equation 4.49, the sum limits should be from i=k+1 to n, and the subscript on the U^T terms should be .,i-k.

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On page 113, in Equation 4.61, the subscript on the U^T terms should be .,i-k.

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On page 107 the last sentence may be clearer to readers not used to seeing units in expressions when written as:

…generated with N(0,(2 x 10^{-4})^2) (in units of seconds) noise added.

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As with the last erratum, the caption for Figure 2.12 on page 78 tmay be clearer to readers not used to seeing units in expressions when written as:

…plus independent N(0,0.05^2) (in units of seconds) noise.

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On page 67, second paragraph from the bottom of the page, the text should read:

…we could set \delta equal to (m – n)^{1/2}…

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On page 11, first line: “can by solved by” should be “can be solved by”

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On page 16, caption for Figure 1.10, the caption should state “n=m” rather than “n=2m”.

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On page 21, first line of (1.58), the last term shoudl be “x*sin(pi xi)” rather than “s*sin(pi xi)”.

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On page 166, (6.95) is missing a G^T, which should be inserted after the omega and before the parenthedical residual term.

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On page 154 (Algorithm 6.4) note that steps 1 and 4 have incorrect signs. The correct steps are:

  1. In algorithm 6.4, step 1:p(k)=+r(k)+beta(k-1)*p(k-1)
  2. In algorithm 6.4, step 4:r(k+1)=r(k)-alpha(k)*A*p(k)

The derivation on pages 150-154 prior to this algorithm is correct.

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The $\DELTA t$ in equation 1.48 should not be in the exponent.

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On page 61, Table 3.1, Last row : Size of Generalized inverse of m should be n by 1,  not m by 1.

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On page 301, last term of equation(A.70) right hand side, includes vector w_p. but the terms should terminate at w_{p-1}.

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