§3 Jacobi法和 Gauss- Seidel法 k Jacobi Gauss-Seidelliterative Methods >Jacobi lterative method -(-a1 1 x+b aux,+au2x2 +.+anxn=b a,,x、n…飞M七=b,n≠0 x,= (-a b2) 1 a 十…十a…x ( .x,+ 写成矩阵形式: Ax=b冷(D+L+U)x=b U 分D=-(L+U)x+b →x=-D(L+U)x+Db B Jacobi迭代阵 x (k+1) -D(L+U)x(k) +D b§3 Jacobi 法和 Gauss - Seidel 法 /* Jacobi & Gauss-Seidel Iterative Methods */ ➢ Jacobi Iterative Method       + + + = + + + = + + + = n n nn n n n n n n a x a x a x b a x a x a x b a x a x a x b ... ... ... ... ... ... ... 1 1 2 2 21 1 22 2 2 2 11 1 12 2 1 1 ( ) ( )  ( )         = − − − + = − − − + = − − − + n nn− n− n nn n n n n n a x a x b a x a x a x b a x a x a x b a x 1 1 1 1 2 1 1 2 2 2 2 2 1 2 2 1 1 1 1 1 ... 1 ... ... ... ... ... 1 ... 1  0 ii a 写成矩阵形式： A = L U D Dx L U x b Ax b D L U x b         = − + + =  + + = ( ) ( ) x D L U x D b   1  1 ( ) − −  = − + + B f  Jacobi 迭代阵 x D L U x D b k k  ( 1) 1 ( ) 1 ( ) + − − = − + +