Mathematics â€ș Numerical Analysis

Iterative Methods for Nonlinear Equations

Description

This cluster of papers focuses on the convergence analysis and improvement of iterative methods, particularly Newton's method, for solving nonlinear equations. It explores higher-order methods, quadrature formulas, local convergence in Banach spaces, and derivative-free approaches to handle multiple roots.

Keywords

Newton's Method; Iterative Methods; Convergence Analysis; Nonlinear Equations; Higher-Order Methods; Quadrature Formulas; Local Convergence; Multiple Roots; Derivative-Free Methods; Banach Spaces

Most Cited Works

Action Title Date Authors
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Handbook of Global Optimization 1995-01-01 Reiner Horst PĂŁnos M. Pardalos
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Interpolation and Approximation by Rational Functions in the Complex Domain 1935-12-31 J. L. Walsh
The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue 1996-01-01 Roelof Koekoek René F. Swarttouw
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SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS 2006-04-19 Ji‐Huan He
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Approximate analytical solution for seepage flow with fractional derivatives in porous media 1998-12-01 Ji‐Huan He
A class of methods for solving nonlinear simultaneous equations 1965-01-01 C. G. Broyden
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Variational iteration method – a kind of non-linear analytical technique: some examples 1999-07-01 Ji‐Huan He
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Some methods of speeding up the convergence of iteration methods 1964-01-01 B. T. Polyak
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A nonsmooth version of Newton's method 1993-01-01 Liqun Qi Jie Sun
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Applied numerical analysis 2005-06-01 Curtis F. Gerald Patrick O. Wheatley
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Fractional Calculus in Bioengineering 2007-02-12 Bruce J. West
A Limited Memory Algorithm for Bound Constrained Optimization 1995-09-01 Richard H. Byrd Peihuang Lu Jorge Nocedal Ciyou Zhu
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Homotopy perturbation method: a new nonlinear analytical technique 2002-10-07 Ji‐Huan He
Conditioning of quasi-Newton methods for function minimization 1970-01-01 David F. Shanno
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind 1962-01-01 David Lee Phillips
Function minimization by conjugate gradients 1964-02-01 R. Fletcher
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Convergence acceleration of iterative sequences. the case of scf iteration 1980-07-01 Péter Pulay
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The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate 1973-04-01 Gene H. Golub VĂ­ctor Pereyra
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Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions 1998-01-01 Jeffrey C. Lagarias James A. Reeds Margaret H. Wright Paul E. Wright
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The Special Functions and Their Approximations 1972-01-01 C. W. Clenshaw Yudell L. Luke
A family of variable-metric methods derived by variational means 1970-01-01 Donald Goldfarb
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Restart procedures for the conjugate gradient method 1977-12-01 M. J. D. Powell
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Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations 1968-09-01 Herbert L. Stone
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Iterative Methods for the Solution of Equations. 1967-03-01 David M. Young J. F. Traub
On the limited memory BFGS method for large scale optimization 1989-08-01 Cheng‐Di Dong Jorge Nocedal
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Multiplier and gradient methods 1969-11-01 Magnus R. Hestenes
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Quasi-Newton Methods, Motivation and Theory 1977-01-01 J. E. Dennis Jorge J. MorĂš
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The method of moving asymptotes—a new method for structural optimization 1987-02-01 Krister Svanberg
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A new definition of fractional derivative 2014-01-16 Roshdi Khalil Mohammed Al Horani A. Yousef Mohammad Sababheh
Recent history of fractional calculus 2010-06-01 J. A. Tenreiro Machado Virginia Kiryakova Francesco Mainardi
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Two-Point Step Size Gradient Methods 1988-01-01 Jonathan Barzilai Jonathan M. Borwein
Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix 1950-03-01 Jack E. Sherman Winifred J. Morrison
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On conformable fractional calculus 2014-10-29 Thabet Abdeljawad
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A coupling method of a homotopy technique and a perturbation technique for non-linear problems 2000-01-01 Ji‐Huan He
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Monotone Piecewise Cubic Interpolation 1980-04-01 F.N. Fritsch R.E. Carlson
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Finite difference approximations for fractional advection–dispersion flow equations 2004-03-17 Mark M. Meerschaert Charles Tadjeran
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Inexact Newton Methods 1982-04-01 Ron S. Dembo Stanley C. Eisenstat Trond Steihaug
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An efficient method for finding the minimum of a function of several variables without calculating derivatives 1964-02-01 M. J. D. Powell
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Iterative methods for linear and nonlinear equations 1996-04-01 C. T. Kelley
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Homotopy perturbation technique 1999-08-01 Ji‐Huan He
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On orthogonal polynomials 1975-12-01 P. TĂșrĂĄn
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The Mathematics of Diffusion. 1957-03-01 J. W. Westwater H. G. Drickamer
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Special Functions and their Applications 1966-01-01 Y. L. L. Nikolai Lebedev Richard A. Silverman
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Advances in Fractional Calculus 2007-01-01 Jocelyn Sabatier Om P. Agrawal J. A. Tenreiro Machado
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A new collection of real world applications of fractional calculus in science and engineering 2018-04-24 HongGuang Sun Yong Zhang Dumitru Băleanu Wen Chen YangQuan Chen
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A Note on the Multiplying Factors for Various χ2 Approximations 1954-07-01 M. S. Bartlett
New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model 2016-01-01 Abdon Atangana Dumitru Băleanu
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The Interpretation of Dummy Variables in Semilogarithmic Equations 1980-01-01 Robert Halvorsen Raymond B. Palmquist
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Iterative Solution of Nonlinear Equations in Several Variables 1971-04-01 E. I. J. M. Ortega Werner C. Rheinboldt
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Applications of Fractional Calculus in Physics 2000-03-01 R. Hilfer

Most Recent Works

Action Title Date Authors
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Variable fractional modeling of nonlinear Gilson–Pickering equation via discrete singular convolution method 2025-04-18 Ola Ragb M. S. Matbuly Mustafa İnç Shahram Rezapour Mohamed Salah
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Approximation of Fractional Caputo Derivative of Variable Order and Variable Terminals with Application to Initial/Boundary Value Problems 2025-04-22 Paulina Stempin Wojciech Sumelka
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On partial Caputo fractional models 2025-04-22 Julia Calatayud Marc Jornet Carla M.A. Pinto
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Solving Time-Fractional Fisher Models by Non-Polynomial Splines in Terms of Logarithmic Derivatives 2025-04-23 H. M. Srivastava Majeed A. Yousif Pshtiwan Othman Mohammed Thabet Abdeljawad Dumitru Bǎleanu Nejmeddine Chorfi
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Local convergence of seventh-order iterative method under weak conditions and its applications 2025-04-23 Dongdong Ruan Xiaofeng Wang Yan Wang
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Novel Forms of Fuzzy Math on Rational Homotopy Theory 2025-04-23 Assist. Lecturer Riyam Abd Al-kareem Bader
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Hermite Polynomials for Solving Volterra-Fredholm Integro-Differential Equations 2025-04-23 Wafaa Abd Ibrahim Marwa Ahmed Jawad Lamyaa H. Ali
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A mathematical analysis of human papilloma virus (HPV) disease with new perspectives of fractional calculus 2025-04-23 Thabet Abdeljawad Nadeem Alam Khan Bahaaeldin Abdalla Asma Al-Jaser Manar A. Alqudah Kamal Shah
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Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations 2025-04-24 Janak Raj Sharma Harmandeep Singh Sunil Kumar
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A numerical scheme to simulate the distributed-order time 2D Benjamin Bona Mahony Burgers equation with fractional-order space 2025-04-24 Hadis Azin Omid Baghani Ali Habibirad
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A Lower Bound Estimate for the Uniform Norm of a Linear Combination of Complex Polynomials 2025-04-24 Khangembam Babina Devi Barchand Chanam
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Study and Analysis of Taylor’s Series using The Modified Conformable Operator 2025-04-24 Ahmed Bouchenak Fakhreddine Seddiki Lahcene Rabhi
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On the Laplace Residual Series Method and Its Application to Time-Fractional Fisher’s Equations 2025-04-24 Rawya Al‐deiakeh Sharifah E. Alhazmi Shrideh Al‐Omari Mohammed Al‐Smadi Shaher Momani
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Global Convergence of Hessenberg Shifted QR III: Approximate Ritz Values via Shifted Inverse Iteration 2025-04-24 Jess Banks Jorge Garza-Vargas Nikhil Srivastava
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Spectral error bound in the mollification of Fourier approximation using Gegenbauer polynomial based mollifier 2025-04-25 P. Megha G. Chandhini
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Mathematical modelling of membrane oscillatory processes in a nonlinear viscoelastic medium via the Caputo-Fabrizio fractional operator 2025-04-25 Andriy Chaban Marek Lis Andriy Lozynskyy ĐŸĐ”Ń‚Ń€ĐŸ ПуĐșач Andrzej Szafraniec Myroslava Vovk
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Study of Solution as Locally Asymptotic Attractivity for Nonlinear Functional Integral Equation 2025-04-26 S. N. Salunkhe
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Fractional Operator Approach and Hybrid Special Polynomials: The Generalized Gould–Hopper–Bell-Based Appell Polynomials and Their Characteristics 2025-04-25 Rabeb Sidaoui E. I. Hassan Abdulghani Muhyi Khaled Aldwoah Alnadhief H. A. Alfedeel Khidir Shaib Mohamed Alawia Adam
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$$H^{1}$$-norm Analysis of an Integral-Averaged L1 Method on Nonuniform Time Meshes for a Time-Fractional Diffusion Problem 2025-04-25 Zi-Yun Zheng Yuan-Ming Wang
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Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point Scheme 2025-04-25 Reza Mollapourasl Joseph Siebor
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Binary Regular ^ Generalized Continuous and Irresolute Functions 2025-04-25 D. Savithiri
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A One-Step Modified New Iterative Method for Solving Partial Differential Equation 2025-04-28 Ibrahim Abdulmalik A. M. Kwami J. O. Okai Aminu Barde Ogboche Abichele Adejoh Jeremiah
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A truncated three-term derivative-free projection method and its inertial-relaxed improvement for nonlinear monotone equations 2025-04-29 Pengjie Liu
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On Extended Numerical Discretization Technique of Fractional Models with Caputo-Type Derivatives 2025-04-28 Reem Allogmany S.S. Alzahrani
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An Inexact \({q}\)-Order Regularized Proximal Newton Method for Nonconvex Composite Optimization 2025-04-28 Ruyu Liu PAN SHAO-HUA Yitian Qian
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(q,h)-Bernstein Bases and Basic Hypergeometric Series 2025-04-29 Fatma ZĂŒrnacı
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The Application of Abstract Algebra in Operational Calculus 2025-04-30 Rong Jiang Tianyi Zhou Yajun Yin
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Approximate Solutions of Nonlinear Integral Equations Using the Cubic B-Spline Scaling Method 2025-04-28 Mohammed Jabbar Adaay Al-Sharea
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A Globally Convergent Conjugate Gradient Method Incorporating Perry’s Parameter for Unconstrained Optimization 2025-05-01 Hasan Jameel Alaa Luqman Ibrahim Neven E. Zaya
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Development of the Nystr\"{o}m Method for Weakly Singular Functional Integral Equations 2025-05-01 Parviz Darania Bahaa Hussain Alrikabi S. Pishbin
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An Iterative Fractional Operational Matrix Method for Solving Fractional Undamped Duffing Equation with High Nonlinearity 2025-05-01 Muhammed I. Syam Sharadga Mwaffag Ishak Hashim Mohd Almie Alias Mohammed M. A. Abuomar Shaher Momani
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A Computational Analysis of Convection-Diffusion Model with Memory using Caputo-Fabrizio Derivative and Cubic Trigonometric B-Spline Functions 2025-05-01 Imtiaz Ahmad Muhammad Hassan Saleem Arshed Ali Aziz Khan Thabet Abdeljawad
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An Innovative Analytical Result of Two-Dimensional Heat Equation Using Joint Mechanism of Natural Transform and Adomian Decomposition Method 2025-05-01 Muhammad Usman Hidayat Ullah Khan Muhammad Sarwar Nahid Fatima Kamaleldin Abodayeh
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Monotonicity of three functions involving the confluent hypergeometric functions of the second kind 2025-04-30 Zhong-Xuan Mao Jing-Feng Tian
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SzegƑ quadrature formulas associated with the weight function $$1+\cos (m\theta )$$ with application to the approximation of certain Christoffel transformations on the interval 2025-05-01 Ruymán Cruz‐Barroso Michael Díaz-Bautista
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Quantum interior point methods 2025-04-24
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APPLICATION OF THE SOME BLAISE ABBO METHOD (SBA) FOR SOLVING THE NONLINEAR FRACTIONAL SCHRÖDINGER EQUATIONS 2025-05-02 Rashid Ali Gires Dimitri Nkaya Joseph Bonazebi Yindoula Massamba Alphonse
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Some Robust Numerical Schemes and Analysis for Solving Time Fractional Nagumo Equation 2025-05-03 Sobin Thomas S. Karthik Suresh Kumar Nadupuri
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Convergence Analysis For Numerical Solution of Integral Equations Using Galarkin Method with two Orthogonal Polynomials 2025-04-30 Ezatullah Haleem Ahad Khan Pyawarai MOHAMMAD DAUD AHMADZAI IRSHAD SALARZAI
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Efficient Numerical Quadrature for Highly Oscillatory Integrals with Bessel Function Kernels 2025-05-03 Guo He Yuying Liu
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Solving Quadratic Equations with Complex Coefficients & Determining the Square Root for any Complex Number 2025-05-05 Aziz Arbai Amina Bellekbir Abounaima Mohammed Chaouki
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Representation of a trigonometric integral via combinatorial sums 2025-05-06
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A Newton-type Method for Non-smooth Under-determined Systems of Equations 2025-05-06 Titus PinĆŁa
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Two-step inexact Newton-like method for solving generalized inverse eigenvalue problems 2025-05-01 Liuqing Hua Wei Ma
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Lie symmetry analysis and solutions for a fractional Riccati–Bernoulli equation 2025-05-01 Shaoru Liu Yanbo Hu
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Fractal Self‐Adjoint Higher Order Boundary‐Value Problems 2025-05-07 Bilender P. Allahverdiev HĂŒseyin Tuna
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Neural network-driven adaptive parameter selection for the Local Method of Fundamental Solutions 2025-05-09 Liang Han Min Lei Chih‐Che Wu Ruiping Niu Heming Jia Hongwei Wang
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A lower bound for the Lebesgue constant of the Morrow-Patterson points 2025-05-01 Tomasz Beberok
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A partial-sum deformation for a family of orthogonal polynomials 2025-05-01 Erik Koelink Pablo RomĂĄn Wadim Zudilin
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Certain new formulas for bibasic Humbert hypergeometric functions $$\Psi _{1}$$ and $$\Psi _{2}$$ 2025-05-10 Ayman Shehata