MATH221 · Annotated SlidesChapter 2 — Error Analysis for Iterative Methods
Chapter 2 · Annotated slides

Error Analysis for Iterative Methods

Order of convergence (linear vs. quadratic, asymptotic error constant), multiple roots and the modified Newton method.

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Slide 1: 2.4
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    Slide 2: 1. Order of Convergence of a Sequence
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      Slide 3: Order of Convergence
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      1. Order α: |pₙ₊₁ − p| / |pₙ − p|^α → λ. α = 1 linear, α = 2 quadratic.
      🎯 How this can come up · 1 question
      MCQ

      Newton’s method near a simple root converges:

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              Slide 8: 2.4 Exercise-7(a)
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                Slide 9: 2.4 Exercise-8(a)
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                  Slide 10: 2.4 Exercise-8(b)
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                      Slide 12: Modified N ewton’s Method
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                      1. At a multiple root Newton is only linear; modified Newton uses μ = f/f′: pₙ = pₙ₋₁ − f f′/((f′)² − f f″).
                      Slide 13: • Use Modified Newton’s method to find solutions accurate to
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