The overall algorithm for solving (4.1) is to (i) compute the recurrence coefficients associated with [[mu].sub.n] in (4.5) via quadratic measure modifications, (ii) compute order-N [[mu].sub.n]-Gaussian quadrature nodes and weights [z.sub.j,N] and [v.sub.j,N], respectively, (iii) identify m such that (4.3) holds so that x+ may be computed in (4.4), and (iv) iteratively apply the bisection algorithm
with the initial interval defined by x+ using the evaluation procedures for [F.sub.n] outlined in Section 3.
Kim, "ISAR cross-range scaling using iterative processing via principal component analysis and bisection algorithm
," IEEE Transactions on Signal Processing, vol.
Compute B and [lambda], [F.sup.(n)] [left arrow] [F.sub.opt] and [Q.sup.(n).sub.1] [left arrow] [Q.sub.1,opt], [Q.sup.(n).sub.2] [left arrow] [Q.sub.2,opt] [lambda] should be chosen from bisection algorithm
and satisfied with [mathematical expression not reproducible] could be obtained by substituting [lambda] into (30), and then [[LAMBDA].sup.2.sub.F], F, [Q.sub.1], and [Q.sub.2] will be gotten as follows.
Use bisection algorithm
to determine corrected maximal [[??].sub.[DELTA]] with tolerance of 0.0001.
As an example, steps of this bisection algorithm
to optimize [gamma] include the following.
Again, the solution to the problem (17a)-(17c) can be obtained by using a standard bisection algorithm
compute [sup.t+[DELTA]t][[bar.[sigma]].sup.(k)]; here, one step of a bisection algorithm
is used; if [sup.t+[DELTA]t][[bar.[sigma]].sup.(k)] does not represent (to a specified tolerance) the solution, go to (2),
For d = 2, the bisection algorithm
from  is used.
Then, given [P.sub.S] at S and considering the constraint [T.sub.R], the optimal [P.sup.o.sub.R] at R can be achieved by the bisection algorithm
, which will be described in the subalgorithm of Algorithm 1.
In Theorem 3.1, which is used in the following to find the number v([lambda]), formula (3.10) requires one multiplication less for the semiseparable case, and this is why the bisection algorithm
works 10% faster than for quasiseparable matrices.
The bisection algorithm
of Gu  keeps only an upper bound on the distance to uncontrollability.
"Improving the performance of the Kernighan-Lin and simulated annealing graph bisection algorithms
," in Proc.