§(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.