[1] Polynomial rooting direction-finding (DF) algorithms are a computationally efficient alternative to search-based DF algorithms and are particularly suitable for uniform linear arrays of physically identical elements provided that mutual interaction among the array elements can be either neglected or compensated for. A popular algorithm in such situations is Root Multiple Signal Classificati...

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 ...

Given a degree n univariate polynomial f(x), the Budan-Fourier function Vf (x) counts the sign changes in the sequence of derivatives of f evaluated at x. The values at which this function jumps are called the virtual roots of f , these include the real roots of f and any multiple root of its derivatives. This concept was introduced (by an equivalent property) by Gonzales-Vega, Lombardi, Mahé i...

A parallel implementation of root finding on an SIMD application accelerator is reported. These are roots of stochastic differential equations in the computational finance domain which require a stochastic simulation to be performed for each evaluation of the pricing function. Experiments show that a speedup of 15X can be achieved over using a stand-alone CPU processor, depending on the require...

A one parameter family of iteration functions for finding roots is derived. ] h e family includes the Laguerre, Halley, Ostrowski and Euler methods and, as a limiting case, Newton's method. All the methods of the family are cubically convergent for a simple root (except Newton's which is quadratically convergent). The superior behavior of Laguerre's method, when starting from a point z for whic...

The Robbins-Monro procedure (1951) for stochastic root-finding is a nonparametric approach. Wu (1985, 1986) has shown that the convergence of the sequential procedure can be greatly improved if we know the distribution of the response. Wu’s approach assumes a parametric model and therefore its convergence rate slows down when the assumed model is very different from the true model. This article...

Quasipolynomials arise in a number of applications, and in particular as the characteristic equation associated with systems of delay differential equations. Quasipolynomial equations are generally difficult to solve, and most often must be solved numerically. In the non-trivial case, quasipolynomials have an infinite number of roots in the complex plane. We present a new numerical method for f...