Parallele Forward-Substitution

Prozessor P_i kennt Spalte i von U (= Zeile i von U ^T).

FOR ALL 0 $\leq$ i $\leq$ n - 1 DO IN PARALLEL
     P_i : tmp[i] := b[i]
END
FOR j := 0 TO n-1 DO
     FOR ALL j $\leq$ i $\leq$ n - 1 DO IN PARALLEL
         P_i : falls i = j: y[i] := tmp[i]/u[i,i];
                 verschicke y[i];
             falls i > j: erhalte y[j];
                 reiche ggf. weiter;
                 tmp[i] := tmp[i]-u[j,i]*y[j];