MATH221 · Chapter 2 · Annotated SlidesAccelerating Convergence
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Accelerating Convergence

Aitken's Δ² method and Steffensen's method for accelerating linearly convergent sequences.

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All 23 slides
  1. 1 CHAPTE
  2. 2 Slide 2
  3. 3 EXERCISE SET 2.5
  4. 4 Slide 4
  5. 5 Slide 5
  6. 6 Slide 6
  7. 7 Slide 7
  8. 8 Slide 8
  9. 9 Slide 9
  10. 10 SteffensenÕs Method
  11. 11 Slide 11
  12. 12 Guidelines
  13. 13 Slide 13
  14. 14 Slide 14
  15. 15 Step 6
  16. 16 Slide 16
  17. 17 Slide 17
  18. 18 Slide 18
  19. 19 Example 7
  20. 20 Fill in the table by repeating the steps.
  21. 21 Slide 21
  22. 22 Steffensen’s Method
  23. 23 Slide 23
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CHAPTE

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Slide 2

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Notes

  1. Aitken's Δ²: p̂ₙ = pₙ − (pₙ₊₁ − pₙ)² / (pₙ₊₂ − 2pₙ₊₁ + pₙ).

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EXERCISE SET 2.5

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SteffensenÕs Method

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Guidelines

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Step 6

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Example 7

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Notes

  1. Steffensen: apply Aitken to fixed-point iterates every third step: quadratic convergence without derivatives.

Exam angle

PredictionQ1

Steffensen's method accelerates:

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Fill in the table by repeating the steps.

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Steffensen’s Method

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