Linear algebra · CMNA Laboratory
Jacobi and Gauss-Seidel both replace a direct solve with a sequence of better guesses. Paste your own matrix into R and watch the residual shrink.
Jacobi computes an entire new approximation from the previous iterate. Gauss-Seidel uses updated components as soon as they become available. That small implementation difference can produce visibly different convergence histories.
Bring your own system
Diagonally dominant systems are especially friendly to these methods. Try changing the matrix and see whether the residual behaves itself.
Preparing R…A and b| n | Jacobi x | Jacobi residual | Gauss-Seidel x | G-S residual |
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