5x1+x2+3x 由原方程{2x1+4x2+x3=2 4x1+6x2+11x3=3 2=(2-2x1-x3) 4 (3-4x1-6x2) (k+1) 3x (k) 2 →{x2 (k+1) (2-2 4 r,(3-4x1 (k)_6x Gauss- Seidel迭代格式: 2 →{x2=(2-2x1-x3) 原方程组为 x (3-4x1-6x2)由原方程 1 2 3 1 2 3 1 2 3 5 3 1 2 4 2 4 6 11 3 x x x x x x x x x  − + + =   + + =   + + =          = − − = − − = − − −  (3 4 6 ) 11 1 (2 2 ) 4 1 (1 3 ) 5 1 3 1 2 2 1 3 1 2 3 x x x x x x x x x          = − − = − − = − − −  + + + (3 4 6 ) 11 1 (2 2 ) 4 1 (1 3 ) 5 1 ( ) 2 ( ) 1 ( 1) 3 ( ) 3 ( ) 1 ( 1) 2 ( ) 3 ( ) 2 ( 1) 1 k k k k k k k k k x x x x x x x x x Gauss-Seidel 迭代格式： 原方程组为          = − − = − − = − − −  (3 4 6 ) 11 1 (2 2 ) 4 1 (1 3 ) 5 1 3 1 2 2 1 3 1 2 3 x x x x x x x x x