Related papers: Annealing approach to root-finding

Deep learning approaches to anomaly detection have recently improved the state of the art in detection performance on complex datasets such as large collections of images or text. These results have sparked a renewed interest in the anomaly…

When Newton's method, or Halley's method is used to approximate the $p${th} root of $1-z$, a sequence of rational functions is obtained. In this paper, a beautiful formula for these rational functions is proved in the square root case,…

This article studies a Newton-like method already used by several authors but which has not been thouroughly studied yet. We call it the robust-variance scoring (RVS) algorithm because the main version of the algorithm that we consider…

This study integrates a data-driven model for estimating the unfrozen water content into the thermo-hydraulic coupling simulation of frozen soils. An artificial neural network (ANN) was employed to develop this data-driven model using a…

We consider minimization of a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of distributed…

Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric…

We propose NAMA (Newton-type Alternating Minimization Algorithm) for solving structured nonsmooth convex optimization problems where the sum of two functions is to be minimized, one being strongly convex and the other composed with a linear…

A damped Newton's method to find a singularity of a vector field in Riemannian setting is presented with global convergence study. It is ensured that the sequence generated by the proposed method reduces to a sequence generated by the…

Purpose: To propose an alternating learning approach to learn the sampling pattern (SP) and the parameters of variational networks (VN) in accelerated parallel magnetic resonance imaging (MRI). Methods: The approach alternates between…

Let f be a polynomial of degree at least 2 with coefficients in a number field K, let x_0 be a sufficiently general element of K, and let alpha be a root of f. We give precise conditions under which Newton iteration, started at the point…

A technique for accelerating global convergence of pseudo-transient continuation Newton methods is proposed based on residual smoothing. The technique is motivated by the effectiveness of local nonlinear smoothers at overcoming strong…

In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…

I am going to provide a new technique of approximating area under the curve, using the Newton-Raphson Method. I am also going to provide a formula that would help us approximate any Definite Integral or help us find the area under the…

Newton-type methods are typically analyzed under Lipschitz continuity of the Hessian, an assumption that can fail for objectives with higher-order or polynomial growth. We introduce a class of nonlinearly preconditioned Newton methods that…

Automatic differentiation through digital signal processing algorithms for virtual analogue modelling has recently gained popularity. These algorithms are typically more computationally efficient than black-box neural networks that rely on…

We introduce a new type of Krasnoselskii's result. Using a simple differentiability condition, we relax the nonexpansive condition in Krasnoselskii's theorem. More clearly, we analyze the convergence of the sequence…

The Richardson-Lucy unfolding approach is simple and excellently performing. It efficiently suppresses artificial high frequency contributions and permits to introduce known features of the true distribution. An algorithm to fix the number…

Anderson Acceleration is a well-established method that allows to speed up or encourage convergence of fixed-point iterations. It has been successfully used in a variety of applications, in particular within the Self-Consistent Field (SCF)…

In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…

In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on…