27 papers · ranked by Valyu relevance
Samuel Lippl, Benjamin Peters, Nikolaus Kriegeskorte, Xiao Luo
Recent work has suggested that feedforward residual neural networks (ResNets) approximate iterative recurrent computations. Iterative computations are useful in many domains, so they might provide good solutions for neural networks to learn. However, principled methods for measuring and manipulating iterative…
Srinivasarao Thota, P. Shanmugasundaram
Objectives This paper proposes three iterative methods of order three, six and seven respectively for solving non-linear equations using the modified homotopy perturbation technique coupled with system of equations. This paper also discusses the analysis of convergence of the proposed iterative methods. Results Several…
Lippl Samuel, Peters Benjamin, Kriegeskorte Nikolaus
Recent work has suggested that feedforward residual neural networks (ResNets) approximate iterative recurrent computations. Iterative computations are useful in many domains, so they might provide good solutions for neural networks to learn. Here we quantify the degree to which ResNets learn iterative solutions and…
Ababu Teklemariam Tiruneh
An iterative formula based on Newton's Method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method has super quadratic convergence of order 2.414 (i.e., 1+ √ ). Newton method is…
Sukhjit Singh, D. K. Gupta
A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen x0, the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total…
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…
Yushi Liu, Yan Wang, Chengzhi Liu, Madhu Chetty
During the iterative process of the progressive iterative approximation, it is necessary to calculate the difference between the current interpolation curve and the corresponding data points, known as the adjustment vector. To achieve more precise adjustments of control points, this paper decomposes the adjustment…
Đặng Quang Á, Quoc Viet Hung Nguyen, Vũ Vinh Quang
In this work, we consider the Dirichlet boundary value problem for nonlinear triharmonic equation. Due to the reduction of the nonlinear boundary value problem to operator equation for the nonlinear term and the unknown second normal derivative we design an iterative method at both continuous and discrete level for…
Rusdrael Antony de Araújo Freire, Francisco Márcio Barboza, Marcelo Barboza
Numerical Approach Authors: ['Rusdrael Antony de Araújo Freire' 'Francisco Márcio Barboza' 'Marcelo Barboza'] This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in…
Srinivasarao Thota, Mohamed M. Awad, P. Shanmugasundaram, Laxmi Rathour
'Laxmi Rathour'] Objective In this paper, we develop a new root-finding algorithm to solve the given non-linear equations. The proposed root-finding algorithm is based on the exponential method. This algorithm is derivative-free and converges fast. Results Several numerical examples are presented to illustrate and…
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…
Ao Li, Robert M. Corless
In the paper "A Chaotic Search for i" ([22]), Strang completely explained the behaviour of Newton's method when using real initial guesses on f(x) = x 2 + 1, which has only a pair of complex roots ±i. He explored an exact symbolic formula for the iteration, namely xn = cot (2n θ0), which is valid in exact arithmetic.…
Yuhao Huang, David L. Chopp
In this paper we propose an improved fast iterative method to solve the Eikonal equation, which can be implemented in parallel. We improve the fast iterative method for Eikonal equation in two novel ways, in the value update and in the error correction. The new value update is very similar to the fast iterative method…
François Rousset, Raphäel Leblois, Arnaud Estoup, Jean-Michel Marin
Simulation-based methods such as approximate Bayesian computation (ABC) are widely used to infer the evolutionary history of populations from molecular genetic data. We describe and evaluate a new iterative method of statistical inference about model parameters, which revisits the idea of inferring a likelihood surface…
Seongtak Kang, Jiho Park, Kyungsoo Kim, Sung-Ho Lim + 3 more
In vivo calcium imaging is a standard neuroimaging technique that allows the simultaneous observation of neuronal population activity. In calcium imaging, the activation signals of neurons are key information for the investigation of neural circuits. For efficient extraction of the calcium signals of neurons, selective…
Alicia Cordero, Eva G. Villalba, Juan R. Torregrosa, Paula Triguero‐Navarro
'Paula Triguero‐Navarro'] In this paper, we construct a derivative-free multi-step iterative scheme based on Steffensen's method. To avoid excessively increasing the number of functional evaluations and, at the same time, to increase the order of convergence, we freeze the divided differences used from the second step…
Elizabeta Šamec, Petra Gidak, Krešimir Fresl
Constrained form-finding results in a nonlinear system of equations unless a linear form-finding method (force density method) is iteratively applied until the given constraints are satisfied. Because the goal of this paper is to contribute to the further development of this method, a brief overview of the method and…
Kazunori D Yamada
In the deep learning era, a gradient descent method is the most common method to optimize parameters of neural networks. Among various mathematical optimization methods, a gradient descent method is the most naive method. Although controlling a learning rate of the method is necessary for quick convergence, the…
Authors not listed
Automated reaction path search based on quantum chemical calculations enables the construction of reaction path networks with minimal prior knowledge. When combined with kinetic simulation on the obtained network, essential mechanistic insights can be extracted to better understand and eventually design novel chemical…
Bin Zhao, John A. Lees, Hongjin Wu, Chao Yang + 1 more
Bacterial genome data are accumulating at an unprecedented speed due the routine use of sequencing in clinical diagnoses, public health surveillance and population genetics studies. Genealogical reconstruction is fundamental to many of these uses, however, inferring genealogy from large-scale genome datasets quickly…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
B. Saheya, Guo-qing Chen, Yun-kang Sui, Cai-ying Wu
This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton’s method to solve it.…
Alexandre Wagemakers, Vipul Periwal
We explore a family of numerical methods, based on the Steffensen divided difference iterative algorithm, that do not evaluate the derivative of the objective functions. The family of methods achieves second-order convergence with two function evaluations per iteration with marginal additional computational cost. An…
Authors not listed
Bottom-up coarse-graining enables efficient simulation of complex molecular systems at mesoscopic scales. Many methods capture structural features well but often overestimate pressure, as computed by the virial theorem, due to thermodynamic representability issues. This limits utility, particularly for studying…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open- source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
AKHIL SHAJAN, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Authors not listed
Efficient and reliable identification of transition states (TS) is critical for reaction modelling. Among the approaches available, the combination of double-ended TS search with eigenvector-following, referred to as “hierarchical TS search”, is an effective tool to locate TSs starting from reactant and product…