The optimal power allocation is computed using the bisection method (relative error below 10−5).
As in the previous application example, we compute the optimal power allocation using the bisection method (relative error below 10−5).
Using the bisection method described in Remark 2.3, we can get a better approximation for such a b.
The significance of qp evaluated as the mid-scale 50 is closely related to the "bisection procedure", where respondents matched, by a sequence of bisections, a number (magnitude) to brightness and loudness.
Thus, we can use the bisection method to find the optimal global multiplier μ [19].
We use the bisection method to solve this constrained optimization problem.
Here, we used the bisection method (Burden and Faires 1985), but any other simple root-finding algorithm might be used.
Then the proposed method estimates the optimal value of by using a standard bisection procedure, and the optimal vectors are calculated for several values of to select maximizing (13), where is a step size and determines the search range of.
We can then estimate the optimal value of τ using a standard bisection procedure, and the optimal vectors x ̂ i, j ( t ) ρ i, j ( t ) are calculated for several values of ρ i, j ( t ) ( = μ y i - R δ, …, μ y i - 2 δ, μ y i - δ, μ y i, μ y i + δ, μ y i + 2 δ, …, μ y i + R δ ) to select x ̂ i, j ( t ) maximizing Equation 15.
Both the two TTO procedures and the discounting part used a bisection procedure, which let subject make a series of choices, while "zooming in" to an indifference value.
