Coupled bisection for root ordering

Coupled bisection for root ordering

We consider the problem of solving multiple ‘‘coupled’’ root-finding problems at once, in that we can evaluate every function at the same point simultaneously. Using a dynamic programming formulation, we show that a sequential bisection algorithm is a close-to-optimalmethod for finding a rankingwith respect to the zeros of these functions. We show the ranking can be found in linear time, prove ...

Generalized Probabilistic Bisection for Stochastic Root-Finding

We consider numerical schemes for root finding of noisy responses through generalizing the Probabilistic Bisection Algorithm (PBA) to the more practical context where the sampling distribution is unknown and location-dependent. As in standard PBA, we rely on a knowledge state for the approximate posterior of the root location. To implement the corresponding Bayesian updating, we also carry out ...

The Bisection Method: Which Root?

A new attitude coupled with the basic thinking to ordering for ranking fuzzy ‎numbers

‎Ranking fuzzy numbers is generalization of the concepts of order, and class, and so have fundamental applications. Moreover, deriving the final efficiency and powerful ranking are helpful to decision makers when solving fuzzy problems. Selecting a good ranking method can apply to choosing a desired criterion in a fuzzy environment. There are numerous methods proposed for the ranking of fuzzy n...

Applications of Continuous Amortization to Bisection-based Root Isolation

Continuous amortization is a technique for computing the complexity of algorithms, and it was first presented by the author in [6]. Continuous amortization can result in simpler and more straight-forward complexity analyses, and it was used in [6, 5, 52] to provide complexity bounds for simple root isolation algorithms. This paper greatly extends the reach of continuous amortization to serve as...