FMM CMSC 878R/AMSC 698R Lect ure 8 Outline N orm of the translat ion operat o r E xam p le of S|R-translation S umm a ry of requirem e nts for functi ons (potentials) that can be used in FMM I dea of a Single Level FMM (SLFMM) S pace division and expansion domains S LFMM algori t hm A sym p totic com p lex ity of SLFMM O ptim ization of SLFMM S|R-operator has almost the same properties as S|S and R|R ( t cannot be zer o) Picture is different. x i x * x i x * x * +t (S| R ) y t ? r 1 ( x * + t ) ? r ( x * ) r r 1 |y - x * - t | < r 1 = | t | - r Since ? r 1 ( x * + t ) ?? r ( t ) ! Origin al exp ansion Is valid only here! Also |x i -x * | < r singular point ! R-expansion S-expansion x * x i R S Exam ple from previous lectures In this case we have Norm of the Translation Operator Active and Passive points of view on translation operator...