Also, we have
A2-'(A2A2 A2A2)
-1
I + 2A1-1 -A1-1
-A1-1 I+2A1- -A,-1
-A-1' I+2A1-1
A1- A1A1 A1A1
x
Aj-1 AIA1 AIA1
A,-1 A1A1 AIA1
= S2
Ai~1 A1A1 A1A1
and then
|IA2 -(A2A2- A2A2)j IIAi-'(A1A1 AiAi)||oo |S211,
= O(At), (5.13)
since |IAi-'(A1A1 AIA1)II| = O(At) by Lemma 5.3.2. From Equation (5.10),
we have the estimate HIC-1Dl, = 1 + O(At).
Three dimensions can be analyzed in the same manner. We write A as a
tridiagonal block matrix with (A2 + 21)'s on the diagonal block and with -I's on
the superdiagonal and subdiagonal block. Write B and A as diagonal matrices with