21 papers · ranked by Valyu relevance
Hong-Yan Zhang, Wei Sun, Xiao Chen, Rui-Jia Lin + 1 more
Kuiper's statistic is a good measure for the difference of ideal distribution and empirical distribution in the goodness-of-fit test. However, it is a challenging problem to solve the critical value and upper tail quantile, or simply Kuiper pair, of Kuiper's statistics due to the difficulties of solving the nonlinear…
Philipp Birken
We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point iteration. Important applications are the Picard iteration and partitioned fluid…
William Gerst
Fixed-point iteration is a technique commonly used for approximating irrational constants, such as calculating the golden ratio φ ≈ 1.618 or finding square roots via the Babylonian method. More generally, the Newton-Raphson method is an iterative process used for estimating the roots of functions, which can be applied…
James R. Riehl, Maxwell I. Zimmerman, Matthew F. Singh, Gregory R. Bowman + 1 more
Equilibria, or fixed points, play an important role in dynamical systems across various domains, yet finding them can be computationally challenging. Here, we show how to efficiently compute all equilibrium points of discrete-valued, discrete-time systems on sparse networks. Using graph partitioning, we recursively…
Dušan Jakovetić, Nataša Krejić, Nataša Krklec Jerinkić, Greta Malaspina + 1 more
'Greta Malaspina' 'Alessandra Micheletti'] We present a class of iterative fully distributed fixed point methods to solve a system of linear equations, such that each agent in the network holds one of the equations of the system. Under a generic directed, strongly connected network, we prove a convergence result…
Mingliang Yu, Xueyuan Nie, Guowei Yang, Peinan Zhong
The fluid structure interaction analysis for structures exhibiting large deformations is carried out by using a strong coupling method, in which a fixed point method with Aitken’s dynamic relaxation is employed to accelerate convergence of the coupling iteration, and geometrically exact beam approach initiated by Simo…
Ankush Aggarwal, Sanjay Pant
Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often leading to slow convergence or even divergence. In this paper, we present a new class…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…
Mario Amrein
In this paper we study the behavior of finite dimensional fixed point iterations, induced by discretization of a continuous fixed point iteration defined within a Banach space setting. We show that the difference between the discrete sequence and its continuous analogue can be bounded in terms depending on the mesh…
Leendert van Maanen, Ritske de Jong, Hedderik van Rijn, Jesus Gomez-Gardenes
'Jesus Gomez-Gardenes'] When multiple strategies can be used to solve a type of problem, the observed response time distributions are often mixtures of multiple underlying base distributions each representing one of these strategies. For the case of two possible strategies, the observed response time distributions obey…
Jesse A Sharp, Kevin Burrage, Matthew J Simpson
Optimal control theory provides insight into complex resource allocation decisions. The forward-backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems (TPBVPs) arising from the application of Pontryagin’s Maximum Principle (PMP) in optimal control. In this…
Itay Dalmedigos, Guy Bunin
We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio of realized species diversity to the number of resources. This ratio is set by…
Stefan M. Filipov, Ivan Gospodinov, István Faragó
This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem…
Francisco I. Chicharro, Alicia Cordero, Juan R. Torregrosa
The complex dynamical analysis of the parametric fourth-order Kim's iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated with the free critical points have been analyzed, showing the stable (and…
Fiza Zafar, Nusrat Yasmin, Saima Akram, Moin-ud-Din Junjua
We construct a new general class of derivative free n-point iterative methods of optimal order of convergence 2n−1 using rational interpolant. The special cases of this class are obtained. These methods do not need Newton's iterate in the first step of their iterative schemes. Numerical computations are presented to…
Fazlollah Soleymani, Stanford Shateyi, Gülcan Özkum
We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the…
Authors not listed
Quantities calculated from molecular simulations are often subject to an initial bias due to unrepresentative starting configurations. Initial data are usually discarded to reduce bias. Chodera's method for automated truncation point selection [J. Chem. Theory Comput. 2016, 12, 4, 1799–1805] is popular but has not been…
Elena Zamaraeva, Christopher M. Collins, Dmytro Antypov, Vladimir V. Gusev + 6 more
Crystal Structure Prediction (CSP) is a fundamental computational problem in materials science. Basin-hopping is a prominent CSP method that combines global Monte Carlo sampling to search over candidate trial structures with local energy minimisation of these candidates. The sampling uses a stochastic policy to…
Srinivasarao Thota, Vivek Kumar Srivastav
Objectives The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton-Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the…
Yasir Nawaz, Muhammad Shoaib Arif, Kamaleldin Abodayeh, Muhammad Usman Ashraf + 1 more
'Muhammad Usman Ashraf' 'Mehvish Naz'] This article suggests a fourth-order numerical approach for solving ordinary differential equations (ODEs) that are both linear and nonlinear. The suggested scheme is an explicit predictor-corrector scheme. For linear ODE, the proposed numerical scheme's stability area is…
Shin-ichi Koda, Shinji Saito
Rapid generation of a plausible reaction path connecting a given reactant and product in advance is crucial for the efficient computation of precise reaction paths or transition states. We propose a computationally efficient potential energy based on molecular structure to generate such paths. This potential energy has…