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.
The Jacobi and Gauss–Seidel Iterative Techniques
The Jacobi and Gauss–Seidel iterative techniques and their convergence.
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7.3
Slide 2
Notes
Jacobi: xᵢ⁽ᵏ⁾ = (bᵢ − Σ_{j≠i} aᵢⱼxⱼ⁽ᵏ⁻¹⁾)/aᵢᵢ (all old values).
Slide 3
The Gauss-Seidel Method
Notes
Gauss–Seidel: uses the newest values as soon as they are computed; usually faster. Both converge if A is strictly diagonally dominant.
Memory trick Jacobi = old values; Gauss–Seidel = newest values.
Exam angle
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