Related papers: The multivariate bisection algorithm
The probabilistic bisection algorithm (PBA) solves a class of stochastic root-finding problems in one dimension by successively updating a prior belief on the location of the root based on noisy responses to queries at chosen points. The…
In this paper, we present an algorithm which allows us to search for all the bisections for the binomial coefficients $\{\binom{n}{k} \}_{k=0,...,n}$ and include a table with the results for all $n\le 154$. Connections with previous work on…
We propose a constructive proof for the Ambrosetti-Rabinowitz Mountain Pass Theorem providing an algorithm, based on a bisection method, for its implementation. The efficiency of our algorithm, particularly suitable for problems in high…
Given a function f: [a,b] -> R, if f(a) < 0 and f(b)> 0 and f is continuous, the Intermediate Value Theorem implies that f has a root in [a,b]. Moreover, given a value-oracle for f, an approximate root of f can be computed using the…
For a continuous function $f$ defined on a closed and bounded domain, there is at least one maximum and one minimum. First, we introduce some preliminaries which are necessary through the paper. We then present an algorithm, which is…
We present a new algorithm for solving the real roots of a bivariate polynomial system $\Sigma=\{f(x,y),g(x,y)\}$ with a finite number of solutions by using a zero-matching method. The method is based on a lower bound for bivariate…
We propose a generalized version of the bisection method where the cutting point between the two subintervals is chosen at random following an arbitrary distribution. We compute expected convergence rates with respect to any arbitrary a…
In this paper, we explain a new Iterative Method-Fixed Point and develop its convergence theory for finding approximate solutions of nonlinear equations in the setting of Banach spaces. First, we discuss the convergence analysis of our…
In this paper we consider the problem of locating a nonzero entry in a high-dimensional vector from possibly adaptive linear measurements. We consider a recursive bisection method which we dub the compressive binary search and show that it…
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…
We analyze, mainly using bifurcation methods, an elliptic superlinear problem in one-dimension with periodic boundary conditions. One of the main novelties is that we follow for the first time a bifurcation approach, relying on a…
We present a new algorithm for refining a real interval containing a single real root: the new method combines characteristics of the classical Bisection algorithm and Newton's Iteration. Our method exhibits quadratic convergence when…
When used to accelerate the convergence of fixed-point iterative methods, such as the Picard method, which is a kind of nonlinear fixed-point iteration, polynomial extrapolation techniques can be very effective. The numerical solution of…
In this work we discuss a Hamiltonian system of ordinary differential equations under Dirichlet boundary conditions. The system of equations in consideration features a mixed (concave-convex) power nonlinearity depending on a positive…
We give an elementary introduction to some recent polyhedral techniques for understanding and solving systems of multivariate polynomial equations. We provide numerous concrete examples and illustrations, and assume no background in…
This paper addresses non-convex constrained optimization problems that are characterized by a scalar complicating constraint. We propose an iterative bisection method for the dual problem (DualBi Algorithm) that recovers a feasible primal…
In this paper we obtain, for a semilinear elliptic problem in R^N, families of solutions bifurcating from the bottom of the spectrum of $-\Delta$. The problem is variational in nature and we apply a nonlinear reduction method which allows…
An efficient method for finding all real roots of a univariate function in a given bounded domain is formulated. The proposed method uses adaptive mesh refinement to locate bracketing intervals based on bisection criterion for root finding.…
In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and multivariate generalised rational approximation. In the…
We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…