Discrete Inverse Problems: Insight and Algorithms

The book uses the software from Regularization Tools.

Misprints as of April 15, 2015:

• Page 16, line 14 from bottom: "and the two types" should be "the two types"
• Page 24, line 9 from bottom (displayed equation): x_j should be t_j
• Page 27, last line: "we have no information"
• Page 31, line 5: "note that"
• Page 49, third paragraph in Exercise 3.5 should read:
  "Then compute three different exact solutions and the corresponding right-hand sides by means of the three examples provided in gravity. Notice that ..."
• Page 49, line 12 from bottom: after "for n = 32" add "and d = 0.25.
• Page 49, line 9 from bottom: at the end of the exercise add "Start with || e ||₂ = 10^-10."
• Page 80, line 10 from bottom: after "n = 32" add "and example = 3".
• Page 81, third paragraph of Exercise 4.5: "use loglog to plot the corresponding L-curve."
• Page 92, line 5 from botom (displayed equation): in the denominator change λ² to λ⁴.
• Page 96, first displayed equation: I_n-1 should be I_n.
• Page 99, Eq. (5.13): subscript k should be λ
• Page 106, Example 5.2: use n = 64 and η = 0.01.
• Page 123, middle of the page: in the displayed equation for φ_i^(k), σ₁⁴ and σ₁⁶ should be σ_i⁴ and σ_i⁶, respectively.
• Page 131, line 8 from bottom should be: x = x - 0.5*max(x);
• Page 133, line 11 from top: change "50" to "n".
• Page 133, lines 17-18 from bottom: "the previous exercise" should be "exercise 6.3"
• Page 136, below Eq. (7.2): "larger" should be "smaller"
• Page 137, after Eq. (7.5): g_-n+1 should be h_-n+1
• Page 138, Eq. (7.6): h_n/2-1,..,n-1 should be i = 0,1,...,n-1
• Page 139, below the displayed equation: delete "blue" (twice)
• Page 168, lines 2 and 3 from bottom: superscript "(x)" should be "(k)" (twice).

Videos with My Lectures

Suggestion for a Short Course

• Chapter 1
• Chapter 2: sections 2.1, 2.2, 2.3
• Chapter 3: sections 3.1.1, 3.2.1, 3.3, 3.5
• Exercises: 2.2, 2.4, 3.4, 3.5, 3.6

• Chapter 4: sections 4.1, 4.2, 4.3, 4.4, 4.7
• Exercises: 4.1, 4.5, 4.6, 4.7

• Chapter 5: sections 5.1, 5.2, 5.3, 5.4, 5.5, 5.6
• Exercises: 4.2, 5.1, 5.2

• Chapter 7: sections 7.1, 7.2, 7.3, 7.4, 7.10
• Exercises: 7.2, 7.3 (TSVD and Tikhonov only), 7.4

• Chapter 6: sections 6.1, 6.2, 6.3
• Chapter 7: section 7.7
• Exercises: 6.2, 6.3, 6.5, 7.3 (iterative methods), 7.8

Additional Material for a Longer Course

• Chapter 7: sections 7.5, 7.6
• Exercises: 7.5, 7.6, 7.7

• Chapter 8: sections 8.1, 8.2, 8.6
• Exercises: 8.1, 8.3, 8.4