The alternative-triangular inethod 685with
0 8
li = -------
l+w8+±w28~'0 1
(28) l? -=-, 2wwhere an operator B is specified by formula (22). The ratio0
~attains its n1aximal value for(29) W = w 0 =2
18/S.,giving in that case0 2 y'1)
~=l+fo'0 8
(30) l 1 = 2 ( 1 + y'i)) ,Proof Inequalities (25) and (26) together irnply that
(Ry,y) > 8(y,y),
whence it follows that 8 < ~ and 17 < 1.
Before giving further inotivations, we may atte1npt operator (22) in
the fonnWith the relations R > 8E or E < t R in view, we obtain for the operator
B the upper estimateB<-R+wR+--R=^1 w^2 ~ (l -+w+--w^2 ~) R=-R^1
-5 4 8 4 ~. ,
I I
0
yielding the relation R > / 1 B. Formula (31) transforms into
= (E - w Ri) (E - w R2) + 2w R,