命题若引B<1,则迭代法X+)=BX+f收敛 证：由8k)=Bk-1),得 lεkl≤Bεk-lW (k=1,2,3,…) →‖ε川≤‖Bk‖εol IBl<1→ msm‖B1s片0 所以 lim a()0 55 : 由 (k) = B  (k-1),得 ||  (k)|| ≤ || B|| ||  (k-1)|| ( k = 1, 2, 3, ······ ) lim 0 ( )   k k 所以  命题 若||B||<1,则迭代法 X(k+1) =B X(k) +f 收敛 ||  (k)|| ≤ || B||k ||  (0)|| lim || || lim || || || || 0 ( ) (0)       k k k k || B|| < 1 B  