消去过程算法 C11 b (k+1) b (k+1) k+1<i
消去过程算法 (1) (1) (1) 11 1 1 ( ) ( ) ( ) ( ) 1 n k k k k kk kk kn k a a b a a a b + ( 1) ( 1) 0 0 1 , k k ij j k i j n a b + + +
k=1,2,…,n-1 b=b-1b.k+≤n ik -ak/a k+1≤;,j≤n (k) O,k+1st≤n
( ) ( ) ( ) ( ) ( ) ( ) 1 1 , , 1 k k k k k k ij ij i i kj k k i, j n ik ik a a b b l a l b + + = − = − + ( ) 0, 1 k ik a = + k i n k n = − 1,2, , 1 k i, j n + 1 ( ) ( ) k k kk ik ik l a= a
回代过程算法 C1x1+…+a1x+…+a1xn=b1 ···+· ain=b C b (n) x=b
回代过程算法 (1) (1) (1) (1) 11 1 1 1 1 ( ) ( ) ( ) ( 1) ( 1) ( 1) 1 1 1 1 1 i i n n i i i ii i in n i n n n n n n n n n n a x a x a x b a x a x b a x a x b − − − − − − − − + + + + = + + + = + = ( ) ( ) n n a x b nn n n =
x=bola 对于i=n-1,n-2,…,1 x,=(b-2anx/a
( ) ( ) n n x b a n n nn = ( ) ( ) ( ) 1 ( ) , n i i i i i ij j ii j i x b a x a = + = − 对于 i n n = − − 1 , 2 , , 1
例1.用消去法解方程组 x1+2x3=5 x+x=3 x1+2x2+4x3+3x4=17 2+3x4=7
1 3 2 4 1 2 3 4 2 4 2 5 3 2 4 3 17 3 7 x x x x x x x x x x + = + = + + + = + = 例1. 用消去法解方程组