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 [2] 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 [8] 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.
