4.3.3 HOW FAST CAN WE (Web hosting mysql) MULTIPLY? 291 Pass
4.3.3 HOW FAST CAN WE MULTIPLY? 291 Pass 0. Let A[Ol(tk-1, . . . , to) = ut, where t = (tk-I . . . to)z. Pass 1. Set A[~](s~-I, tk-2,. . . , to) + A[ ](O, t,+2,. . . , to) + w(sk- o~~~o)2 . A[O](l, t&s,. . . , to). PaSS 2. Set Ai2](Sk-l, Sk-Z, tk-3,. . . , to) + Ail](S,z-l, 0, tk-3,. . . , to) + W(Sk-2Sk- o 0)2 d](Sk-1, 1, t&3,. . . , to). . . . Pass k. Set A[ ](Sk-1, . . . , Sl, So) + A[k-l](Sk-l,. . . , sl, 0) + W(SoS - Sk- )2 . Aik- ](Sk-l,. . . , Sl, 1). It is fairly easy to prove by induction that we have &l(Sk-l,. . . , Sk-j, tk-j-l,. . . , to) -W(S~S~…Sk- )2.(tk-l…tk-~o…0)2 Ut, (33) c O