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This paper studies the convergence difficulty of cohesive zone models in static analysis. It is shown that an inappropriate starting point of iterations in the Newton-Raphson method is responsible for the convergence difficulty. A simple,…

Computational Physics · Physics 2020-05-07 Reza Sepasdar , Maryam Shakiba

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…

Optimization and Control · Mathematics 2016-09-06 Haishan Ye , Luo Luo , Zhihua Zhang

In this paper we establish an estimate for the rate of convergence of the Krasnosel'ski\v{\i}-Mann iteration for computing fixed points of non-expansive maps. Our main result settles the Baillon-Bruck conjecture [3] on the asymptotic…

Optimization and Control · Mathematics 2013-10-09 Roberto Cominetti , José A. Soto , José Vaisman

We established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative).…

Numerical Analysis · Mathematics 2013-04-18 J. P. Jaiswal , Neha Choubey

The strong contraction mapping, a self-mapping that the range is always a subset of the domain, admits a unique fixed-point which can be pinned down by the iteration of the mapping. We introduce a topological non-convex optimization method…

General Mathematics · Mathematics 2019-03-25 Siwei Luo

We present a rigorous convergence analysis of a new method for density-based topology optimization that provides point-wise bound preserving design updates and faster convergence than other popular first-order topology optimization methods.…

Optimization and Control · Mathematics 2025-02-25 Brendan Keith , Dohyun Kim , Boyan S. Lazarov , Thomas M. Surowiec

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Machine Learning · Computer Science 2022-10-04 Ayano Kaneda , Osman Akar , Jingyu Chen , Victoria Kala , David Hyde , Joseph Teran

This paper presents a modified general viscosity iterative process designed to solve variational inclusion and fixed point problems involving multi-valued quasi-nonexpansive and demi-contractive operators. The modified iterative process…

Optimization and Control · Mathematics 2025-01-14 Furmose Mendy , John T Mendy

Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…

Information Theory · Computer Science 2010-01-13 Florence Alberge , Ziad Naja , P. Duhamel

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

Optimization and Control · Mathematics 2011-01-10 Luis M. Briceño-Arias

We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of…

Numerical Analysis · Mathematics 2023-10-17 Dimitrios Mitsotakis

An iterative formula based on Newton 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…

Numerical Analysis · Mathematics 2012-10-30 Ababu Teklemariam Tiruneh

In this paper, we study a new iterative method for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the frame work of reflexive real Banach spaces. Moreover, we prove the strong convergence theorem for…

Functional Analysis · Mathematics 2015-12-02 Vahid Darvish

Motivated by the success of Sinkhorn's algorithm for entropic optimal transport, we study convergence properties of iterative proportional fitting procedures (IPFP) used to solve more general information projection problems. We establish…

Optimization and Control · Mathematics 2025-04-14 Stephan Eckstein , Aziz Lakhal

A new learning algorithm proposed by Brandt and Lin for neural network [1], [2] has been shown to be mathematically equivalent to the conventional back-propagation learning algorithm, but has several advantages over the backpropagation…

Neural and Evolutionary Computing · Computer Science 2022-02-28 Feng Lin

The present work deals with an improved back-propagation algorithm based on Gauss-Newton numerical optimization method for fast convergence. The steepest descent method is used for the back-propagation. The algorithm is tested using various…

Artificial Intelligence · Computer Science 2012-06-21 Sudarshan Nandy , Partha Pratim Sarkar , Achintya Das

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

Statistics Theory · Mathematics 2007-12-18 Jiming Jiang , Yihui Luan , You-Gan Wang

This paper presents a modification of Secant method for finding roots of equations that uses three points for iteration instead of just two. The development of the mathematical formula to be used in the iteration process is provided…

Numerical Analysis · Mathematics 2019-02-26 Ababu Teklemariam Tiruneh

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how…

Numerical Analysis · Mathematics 2023-01-31 Sohei Arisaka , Qianxiao Li

When proving the correctness of a method for slicing probabilistic programs, it was previously discovered by the authors that for a fixed point iteration to work one needs a non-standard starting point for the iteration. This paper presents…

Programming Languages · Computer Science 2024-12-11 Torben Amtoft , Anindya Banerjee