Subfield · Numerical Analysis
Most cited papers in Numerical Analysis
What are the most cited papers in Numerical Analysis?
The most cited paper in Numerical Analysis is "Adam: A Method for Stochastic Optimization" (Mandi, Jayanta, Canoy, Rocsildes, Bucarey, Víctor et al., 2015), with 50,327 citations. Next come "Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces" (29,587) and "Deterministic Nonperiodic Flow" (19,616).
Showing 50 of 99 papers. Every paper with more than 1,999 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Adam: A Method for Stochastic Optimization Mandi, Jayanta, Canoy, Rocsildes, Bucarey, Víctor et al. · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) | May 2015 | 50,327 |
| 2 | Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces Rainer Storn, Kenneth V. Price · Journal of Global Optimization | Dec 1997 | 29,587 |
| 3 | Deterministic Nonperiodic Flow Edward N. Lorenz · Journal of the Atmospheric Sciences | Mar 1963 | 19,616 |
| 4 | No free lunch theorems for optimization David H. Wolpert, William G. Macready · IEEE Transactions on Evolutionary Computation | Apr 1997 | 14,318 |
| 5 | On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming Andreas Wächter, Lorenz T. Biegler · Mathematical Programming | 28 Apr 2005 | 9,722 |
| 6 | YALMIP : a toolbox for modeling and optimization in MATLAB Johan Löfberg | 21 Mar 2005 | 9,338 |
| 7 | On the limited memory BFGS method for large scale optimization Dong C. Liu, Jorge Nocedal · Mathematical Programming | Aug 1989 | 8,813 |
| 8 | Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones Jos F. Sturm · Optimization methods & software | 1999 | 7,558 |
| 9 | 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 |
| 10 | Ordinary Differential Equations John M. Stewart · Cambridge University Press eBooks | 12 Oct 2017 | 7,320 |
| 11 | Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates Ilya M. Sobol · Mathematics and Computers in Simulation | Feb 2001 | 6,427 |
| 12 | 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 |
| 13 | Harris hawks optimization: Algorithm and applications Ali Asghar Heidari, Seyedali Mirjalili, Hossam Faris et al. · Future Generation Computer Systems | 28 Feb 2019 | 6,334 |
| 14 | Theory of Ordinary Differential Equations Earl A. Coddington, Norman Levinson, Theodor Teichmann · Physics Today | Feb 1956 | 6,268 |
| 15 | Combinatorial Optimization: Algorithms and Complexity. David Johnson, Christos H. Papadimitriou, Kenneth Steiglitz · American Mathematical Monthly | Mar 1984 | 6,041 |
| 16 | Theory of Linear and Integer Programming Adam N. Letchford, Alexander Schrijver · Journal of the Operational Research Society | Jul 2000 | 5,691 |
| 17 | The method of moving asymptotes—a new method for structural optimization Krister Svanberg · International Journal for Numerical Methods in Engineering | Feb 1987 | 5,593 |
| 18 | State-space solutions to standard H/sub 2/ and H/sub infinity / control problems John C. Doyle, K. Glover, Pramod P. Khargonekar et al. · IEEE Transactions on Automatic Control | 1989 | 5,567 |
| 19 | Optimal approximations by piecewise smooth functions and associated variational problems David B. Mumford, Jayant M. Shah · Communications on Pure and Applied Mathematics | Jul 1989 | 5,245 |
| 20 | Function minimization by conjugate gradients Roger Fletcher · The Computer Journal | Feb 1964 | 4,962 |
| 21 | CONTINUOUS INSPECTION SCHEMES E. S. Page · Biometrika | 1954 | 4,771 |
| 22 | Table of Integrals, Series, and Products I. S. Gradshteyn, I.M. RYZHIK, D. F. Hays · Journal of Lubrication Technology | Jul 1976 | 4,749 |
| 23 | Perturbation Methods A. H. Nayfeh, Vimal Singh · IEEE Transactions on Systems Man and Cybernetics | May 1978 | 4,699 |
| 24 | 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 |
| 25 | Benchmarking optimization software with performance profiles Elizabeth D. Dolan, Jorge J. Morè · Mathematical Programming | 2002 | 4,469 |
| 26 | An iteration method for the solution of the eigenvalue problem of linear differential and integral operators Cornelius Lanczos · Journal of research of the National Bureau of Standards | Oct 1950 | 4,448 |
| 27 | LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares Christopher C. Paige, Michael A. Saunders · ACM Transactions on Mathematical Software | Mar 1982 | 4,448 |
| 28 | P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation Berk Hess · Journal of Chemical Theory and Computation | Dec 2007 | 4,177 |
| 29 | A new approach to variable metric algorithms Roger Fletcher · The Computer Journal | Mar 1970 | 4,132 |
| 30 | 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 |
| 31 | Partitioning procedures for solving mixed-variables programming problems J. F. Benders · Numerische Mathematik | Dec 1962 | 3,886 |
| 32 | Semidefinite Relaxation of Quadratic Optimization Problems Zhi-Quan Tom Luo, Wing‐Kin Ma, Anthony Man–Cho So et al. · IEEE Signal Processing Magazine | 23 Apr 2010 | 3,769 |
| 33 | An integrable shallow water equation with peaked solitons Roberto Camassa, Darryl D. Holm · Physical Review Letters | 13 Sep 1993 | 3,754 |
| 34 | Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming Michel X. Goemans, David P. Williamson · Journal of the ACM | Nov 1995 | 3,723 |
| 35 | A family of embedded Runge-Kutta formulae John R. Dormand, P.J. Prince · Journal of Computational and Applied Mathematics | Mar 1980 | 3,681 |
| 36 | Reversible multiple time scale molecular dynamics Mark E. Tuckerman, B. J. Berne, Glenn J. Martyna · The Journal of Chemical Physics | Aug 1992 | 3,655 |
| 37 | The MATLAB ODE Suite Lawrence F. Shampine, Mark W. Reichelt · SIAM Journal on Scientific Computing | 1997 | 3,654 |
| 38 | Algorithm 778: L-BFGS-B Ciyou Zhu, Richard H. Byrd, Peihuang Lu et al. · ACM Transactions on Mathematical Software | Dec 1997 | 3,560 |
| 39 | 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 |
| 40 | Homotopy perturbation technique Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering | Aug 1999 | 3,485 |
| 41 | New development in freefem++ Frédéric Hecht · Journal of Numerical Mathematics | 2012 | 3,447 |
| 42 | Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn et al. · SIAM Journal on Numerical Analysis | 2002 | 3,312 |
| 43 | Difference Methods for Initial-Value Problems Robert D. Richtmyer, E. H. Dill · Physics Today | Apr 1959 | 3,233 |
| 44 | Analysis of Fractional Differential Equations Kai Diethelm, Neville J. Ford · Journal of Mathematical Analysis and Applications | 2002 | 3,200 |
| 45 | Random Number Generation and Quasi-Monte Carlo Methods. Bruce Jay Collings, Harald Niederreiter · Journal of the American Statistical Association | Jun 1993 | 2,965 |
| 46 | The Arithmetic Optimization Algorithm Laith Abualigah, Ali H. Diabat, Seyedali Mirjalili et al. · Computer Methods in Applied Mechanics and Engineering | 12 Jan 2021 | 2,951 |
| 47 | Two-Point Step Size Gradient Methods Jonathan Barzilai, Jonathan Michael Borwein · IMA Journal of Numerical Analysis | 1988 | 2,943 |
| 48 | On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators Jonathan Eckstein, Dimitri P. Bertsekas · Mathematical Programming | Apr 1992 | 2,923 |
| 49 | The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations C. G. Broyden · IMA Journal of Applied Mathematics | 1970 | 2,913 |
| 50 | Optimization of Control Parameters for Genetic Algorithms John J. Grefenstette · IEEE Transactions on Systems Man and Cybernetics | 1986 | 2,869 |
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.