MATH221 · Annotated SlidesChapter 7 — The Jacobi and Gauss–Seidel Iterative Techniques
Chapter 7 · Annotated slides

The Jacobi and Gauss–Seidel Iterative Techniques

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

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    1. Jacobi: xᵢ⁽ᵏ⁾ = (bᵢ − Σ_{j≠i} aᵢⱼxⱼ⁽ᵏ⁻¹⁾)/aᵢᵢ (all old values).
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      Slide 4: The Gauss-Seidel Method
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      1. Gauss–Seidel: uses the newest values as soon as they are computed; usually faster. Both converge if A is strictly diagonally dominant.
      Memory trickJacobi = old values; Gauss–Seidel = newest values.
      🎯 How this can come up · 1 question
      Written

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

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