Bisection
Algorithm
§(a) select an upper bound gu and a lower bound gl such that
gl £ ||G||¥ £ gu
(b)
if (gu-gl)/gl £ specified level, stop; ||G||¥ » (gu+gl)/2. Otherwise go to next step.
(c) set g = (gl + gu) /2;
(d) test if ||G||¥ < g by calculating the
eigenvalues of H with this g;
(e) if H has an eigenvalue on jR set gl = g ; otherwise set gu = g ; go back to step (b).
§In all the subsequent
discussions, WLOG we can assume g = 1 by a suitable scaling since ||G||¥ < g Û || g -1G||¥ <1.
