MATH221 · Chapter 7 · Annotated SlidesThe Jacobi and Gauss–Seidel Iterative Techniques
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The Jacobi and Gauss–Seidel Iterative Techniques

The Jacobi and Gauss–Seidel iterative techniques and their convergence.

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Every original slide is shown unchanged. Yellow marks on a slide point to a numbered note: hover or tap a mark to jump to its note, and hover a note to see its marks. Questions tagged Past exam appeared on a real paper; Prediction questions are likely angles, not confirmed. Pick an answer to each question: a wrong pick tells you why it is wrong, so you can try again.

All 11 slides
  1. 1 7.3
  2. 2 Slide 2
  3. 3 Slide 3
  4. 4 The Gauss-Seidel Method
  5. 5 Slide 5
  6. 6 Slide 6
  7. 7 Slide 7
  8. 8 Slide 8
  9. 9 Slide 9
  10. 10 Slide 10
  11. 11 Slide 11
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7.3

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Slide 2

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Notes

  1. Jacobi: xᵢ⁽ᵏ⁾ = (bᵢ − Σ_{j≠i} aᵢⱼxⱼ⁽ᵏ⁻¹⁾)/aᵢᵢ (all old values).

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The Gauss-Seidel Method

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Notes

  1. Gauss–Seidel: uses the newest values as soon as they are computed; usually faster. Both converge if A is strictly diagonally dominant.

  2. Memory trick Jacobi = old values; Gauss–Seidel = newest values.

Exam angle

PredictionQ1

One Gauss–Seidel step for 10x − y = 9, −x + 10y = 9 from (0, 0).

Compare with the model answer

x = (9 + 0)/10 = 0.9; y = (9 + 0.9)/10 = 0.99.

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