lizfcm/notes/29-Nov.org

Jacobi Iteration (cont.)

x^k+1 = D^-1(b - (L + U)x^k)

{ x^k+1 = x^k + D^-1 r^k r^k = b - Ax^k }

error: || x^k+1 - x^k ||_2 residual: || r^k ||_2

Gauss-Seidel Iteration: A = (L + D + U) ⇒ Ax = b (D + U)x = b - Lx x = (D + U)^-1 (b - Lx)

x^k+1 = (D+U)^-1(b - Lx^k) (D + U)^-1 x (bsubst)