Most cited papers in Iterative Methods for Nonlinear Equations
What are the most cited papers in Iterative Methods for Nonlinear Equations?
The most cited paper in Iterative Methods for Nonlinear Equations is "On the limited memory BFGS method for large scale optimization" (Dong C. Liu, Jorge Nocedal, 1989), with 8,813 citations. Next come "Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions" (7,523) and "A Limited Memory Algorithm for Bound Constrained Optimization" (6,417).
Showing 50 of 100 papers. Every paper with more than 607 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | On the limited memory BFGS method for large scale optimization Dong C. Liu, Jorge Nocedal · Mathematical Programming | Aug 1989 | 8,813 |
| 2 | Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions Jeffrey C. Lagarias, James A. Reeds, Margaret H. Wright et al. · SIAM Journal on Optimization | 1998 | 7,523 |
| 3 | A Limited Memory Algorithm for Bound Constrained Optimization Richard H. Byrd, Peihuang Lu, Jorge Nocedal et al. · SIAM Journal on Scientific Computing | Sep 1995 | 6,417 |
| 4 | The method of moving asymptotes—a new method for structural optimization Krister Svanberg · International Journal for Numerical Methods in Engineering | Feb 1987 | 5,593 |
| 5 | Function minimization by conjugate gradients Roger Fletcher · The Computer Journal | Feb 1964 | 4,962 |
| 6 | CONTINUOUS INSPECTION SCHEMES E. S. Page · Biometrika | 1954 | 4,771 |
| 7 | Table of Integrals, Series, and Products I. S. Gradshteyn, I.M. RYZHIK, D. F. Hays · Journal of Lubrication Technology | Jul 1976 | 4,749 |
| 8 | An efficient method for finding the minimum of a function of several variables without calculating derivatives M. J. D. Powell · The Computer Journal | Feb 1964 | 4,668 |
| 9 | New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model Atangana Abdon, Dumitru Bǎleanu · DOAJ (DOAJ: Directory of Open Access Journals) | 2016 | 3,956 |
| 10 | A new definition of fractional derivative Roshdi Rashid Khalil, Mohammed Al Horani, A. Yousef et al. · Journal of Computational and Applied Mathematics | 16 Jan 2014 | 3,504 |
| 11 | Homotopy perturbation technique Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering | Aug 1999 | 3,485 |
| 12 | Two-Point Step Size Gradient Methods Jonathan Barzilai, Jonathan Michael Borwein · IMA Journal of Numerical Analysis | 1988 | 2,943 |
| 13 | Convergence acceleration of iterative sequences. the case of scf iteration Péter Pulay · Chemical Physics Letters | Jul 1980 | 2,644 |
| 14 | Variational iteration method – a kind of non-linear analytical technique: some examples Ji‐Huan He · International Journal of Non-Linear Mechanics | Jul 1999 | 2,553 |
| 15 | Multiplier and gradient methods Magnus Rudolph Hestenes · Journal of Optimization Theory and Applications | Nov 1969 | 2,502 |
| 16 | SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS Ji‐Huan He · International Journal of Modern Physics B | 19 Apr 2006 | 2,215 |
| 17 | On conformable fractional calculus Thabet Abdeljawad · Journal of Computational and Applied Mathematics | 29 Oct 2014 | 2,054 |
| 18 | A Technique for the Numerical Solution of Certain Integral Equations of the First Kind David Lee Phillips · Journal of the ACM | 1962 | 2,042 |
| 19 | Fractional Calculus in Bioengineering Bruce J. West · Journal of Statistical Physics | 12 Feb 2007 | 1,999 |
| 20 | A coupling method of a homotopy technique and a perturbation technique for non-linear problems Ji‐Huan He · International Journal of Non-Linear Mechanics | 2000 | 1,811 |
| 21 | A new collection of real world applications of fractional calculus in science and engineering HongGuang Sun, Yong Zhang, Dumitru Bǎleanu et al. · Communications in Nonlinear Science and Numerical Simulation | 24 Apr 2018 | 1,786 |
| 22 | Restart procedures for the conjugate gradient method M. J. D. Powell · Mathematical Programming | Dec 1977 | 1,726 |
| 23 | Recent history of fractional calculus J. A. Tenreiro Machado, Virginia S. Kiryakova, Francesco Mainardi · Communications in Nonlinear Science and Numerical Simulation | Jun 2010 | 1,638 |
| 24 | On orthogonal polynomials P. Túrán · Analysis Mathematica | Dec 1975 | 1,624 |
| 25 | Homotopy perturbation method: a new nonlinear analytical technique Ji‐Huan He · Applied Mathematics and Computation | 7 Oct 2002 | 1,616 |
| 26 | Quasi-Newton Methods, Motivation and Theory John E. Dennis, Jorge J. Morè · SIAM Review | 1977 | 1,569 |
| 27 | Finite difference approximations for fractional advection–dispersion flow equations Mark M. Meerschaert, Charles Tadjeran · Journal of Computational and Applied Mathematics | 17 Mar 2004 | 1,509 |
| 28 | A nonsmooth version of Newton's method Liqun Qi, Jie Sun · Mathematical Programming | 1993 | 1,495 |
| 29 | Approximate analytical solution for seepage flow with fractional derivatives in porous media Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering | Dec 1998 | 1,298 |
| 30 | A Caputo fractional derivative of a function with respect to another function Ricardo Almeida · Communications in Nonlinear Science and Numerical Simulation | 12 Sep 2016 | 1,283 |
| 31 | A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations Kai Diethelm, Neville J. Ford, Alan D. Freed · Nonlinear Dynamics | Jul 2002 | 1,275 |
| 32 | Application of homotopy perturbation method to nonlinear wave equations Ji‐Huan He · Chaos Solitons & Fractals | 18 May 2005 | 1,258 |
| 33 | Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method F. Durbin · The Computer Journal | Nov 1974 | 1,155 |
| 34 | On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds Thomas F. Coleman, Yuying Li · Mathematical Programming | Oct 1994 | 1,148 |
| 35 | Homotopy perturbation method for solving boundary value problems Ji‐Huan He · Physics Letters A | 14 Oct 2005 | 1,135 |
| 36 | Fractional diffusion and wave equations William R. Schneider, Walter Wyss · Journal of Mathematical Physics | 1989 | 1,130 |
| 37 | A globally convergent method for nonlinear programming S.-P. Han · Journal of Optimization Theory and Applications | Jul 1977 | 1,111 |
| 38 | Isogeometric analysis of structural vibrations J. Austin Cottrell, Alessandro Reali, Yuri Bazilevs et al. · Computer Methods in Applied Mechanics and Engineering | Mar 2006 | 1,103 |
| 39 | Non‐linear Transformations of Divergent and Slowly Convergent Sequences Daniel N. Shanks · Studies in Applied Mathematics | Apr 1955 | 1,098 |
| 40 | Global Convergence Properties of Conjugate Gradient Methods for Optimization Jean Charles Gilbert, Jorge Nocedal · SIAM Journal on Optimization | Feb 1992 | 1,072 |
| 41 | An interior algorithm for nonlinear optimization that combines line search and trust region steps Richard A. Waltz, José Luis Morales, Jorge Nocedal et al. · Mathematical Programming | 24 Nov 2005 | 1,066 |
| 42 | Detailed Error Analysis for a Fractional Adams Method Kai Diethelm, Neville J. Ford, Alan D. Freed · Numerical Algorithms | May 2004 | 1,047 |
| 43 | Iterative Methods for Solving Linear Systems Alfio Maria Quarteroni, Riccardo Sacco, Fausto Saleri · Texts in applied mathematics | 31 Mar 2006 | 1,041 |
| 44 | Iterative Procedures for Nonlinear Integral Equations Donald G. Anderson · Journal of the ACM | Oct 1965 | 1,013 |
| 45 | Numerical methods and software David K. Kahaner, C Moler, Stephen Nash | 1989 | 1,011 |
| 46 | Behaviour of recursive division surfaces near extraordinary points D. Doo, Malcolm A. Sabin · Computer-Aided Design | Nov 1978 | 1,002 |
| 47 | Fractional relaxation-oscillation and fractional diffusion-wave phenomena Francesco Mainardi · Chaos Solitons & Fractals | Sep 1996 | 989 |
| 48 | Generalized Taylor’s formula Zaid Odibat, Nabil T. Shawagfeh · Applied Mathematics and Computation | 12 Sep 2006 | 972 |
| 49 | Formulation of Euler–Lagrange equations for fractional variational problems Om P. Agrawal · Journal of Mathematical Analysis and Applications | Aug 2002 | 957 |
| 50 | An Adaptive Nonlinear Least-Squares Algorithm John E. Dennis, David Michael Gay, Roy E. Walsh · ACM Transactions on Mathematical Software | Sep 1981 | 939 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.