Topic · Numerical Methods and Algorithms
Most cited papers in Numerical Methods and Algorithms
What are the most cited papers in Numerical Methods and Algorithms?
The most cited paper in Numerical Methods and Algorithms is "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming" (Andreas Wächter, Lorenz T. Biegler, 2005), with 9,722 citations. Next come "Mersenne twister" (5,805) and "The Design and Implementation of FFTW3" (5,208).
Showing 50 of 98 papers. Every paper with more than 549 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | 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 |
| 2 | Mersenne twister Makoto Matsumoto, Takuji Nishimura · ACM Transactions on Modeling and Computer Simulation | 1998 | 5,805 |
| 3 | The Design and Implementation of FFTW3 Matteo Frigo, Steven G. Johnson · Proceedings of the IEEE | 24 Jan 2005 | 5,208 |
| 4 | 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 |
| 5 | Algorithm 778: L-BFGS-B Ciyou Zhu, Richard H. Byrd, Peihuang Lu et al. · ACM Transactions on Mathematical Software | Dec 1997 | 3,560 |
| 6 | The CORDIC Trigonometric Computing Technique Jack E. Volder · IRE Transactions on Electronic Computers | Sep 1959 | 2,649 |
| 7 | Matrix multiplication via arithmetic progressions Don Coppersmith, Shmuel Winograd · Journal of Symbolic Computation | Mar 1990 | 2,313 |
| 8 | The FEniCS Project Version 1.5 Martin Sandve Alnæs, Jan Blechta, Johan E. Hake et al. · Department of Earth Sciences EPrints Repository | 2015 | 1,987 |
| 9 | Jacobian-free Newton–Krylov methods: a survey of approaches and applications Dana A. Knoll, David Elliot Keyes · Journal of Computational Physics | 9 Oct 2003 | 1,956 |
| 10 | SDPT3 — A Matlab software package for semidefinite programming, Version 1.3 Kim-Chuan Toh, Michael J. Todd, Reha H. Tütüncü · Optimization methods & software | 1999 | 1,945 |
| 11 | A set of level 3 basic linear algebra subprograms Jack J. Dongarra, Jeremy Du Croz, Sven J. Hammarling et al. · ACM Transactions on Mathematical Software | Mar 1990 | 1,843 |
| 12 | FFTW: an adaptive software architecture for the FFT Matteo Frigo, Steven G. Johnson | 27 Nov 2002 | 1,828 |
| 13 | What every computer scientist should know about floating-point arithmetic David Theo Goldberg · ACM Computing Surveys | Mar 1991 | 1,744 |
| 14 | SymPy: symbolic computing in Python Aaron Meurer et al. · PeerJ Computer Science | 2 Jan 2017 | 1,719 |
| 15 | Basic Linear Algebra Subprograms for Fortran Usage Charles L. Lawson, Richard J. Hanson, David R. Kincaid et al. · ACM Transactions on Mathematical Software | Sep 1979 | 1,641 |
| 16 | The singular value decomposition: Its computation and some applications Virginia C. Klema, Alan J. Laub · IEEE Transactions on Automatic Control | Apr 1980 | 1,631 |
| 17 | Testing Unconstrained Optimization Software Jorge J. Morè, B. S. Garbow, K. E. Hillstrom · ACM Transactions on Mathematical Software | Mar 1981 | 1,529 |
| 18 | Analysis of recursive stochastic algorithms Lennart Ljung · IEEE Transactions on Automatic Control | Aug 1977 | 1,483 |
| 19 | A General Definition of Residuals David Roxbee Cox, E. J. Snell · Journal of the Royal Statistical Society Series B (Statistical Methodology) | Jul 1968 | 1,326 |
| 20 | qpOASES: a parametric active-set algorithm for quadratic programming Hans Joachim Ferreau, Christian Kirches, Andreas Potschka et al. · Mathematical Programming Computation | 29 Apr 2014 | 1,288 |
| 21 | Signed-Digit Numbe Representations for Fast Parallel Arithmetic Algirdas Avižienis · IEEE Transactions on Electronic Computers | Sep 1961 | 1,259 |
| 22 | Torch7: A Matlab-like Environment for Machine Learning Ronan Collobert, Koray Kavukcuoglu, Clément Farabet · Infoscience (Ecole Polytechnique Fédérale de Lausanne) | 2011 | 1,257 |
| 23 | A tutorial on geometric programming Stephen Boyd, Seung-Jean Kim, Lieven Vandenberghe et al. · Optimization and Engineering | Mar 2007 | 1,230 |
| 24 | Power Flow Solution by Newton's Method W.F. Tinney, Clifford Hart · IEEE Transactions on Power Apparatus and Systems | Nov 1967 | 1,220 |
| 25 | Using the matrix pencil method to estimate the parameters of a sum of complex exponentials Tapan K. Sarkar, O.J.B. Almeida Pereira · IEEE Antennas and Propagation Magazine | Feb 1995 | 1,213 |
| 26 | Most Tensor Problems Are NP-Hard Christopher J. Hillar, Lek‐Heng Lim · Journal of the ACM | Nov 2013 | 1,165 |
| 27 | Solving semidefinite-quadratic-linear programs using SDPT3 R. H. T�t�nc�, Kim-Chuan Toh, Michael J. Todd · Mathematical Programming | Feb 2003 | 1,163 |
| 28 | Fast fourier transforms: A tutorial review and a state of the art Pierre Duhamel, Martin Vetterli · Signal Processing | Apr 1990 | 1,153 |
| 29 | A Regular Layout for Parallel Adders Brent, Kung · IEEE Transactions on Computers | Mar 1982 | 1,149 |
| 30 | INTLAB — INTerval LABoratory Siegfried M. Rump | 1999 | 1,148 |
| 31 | A fast sweeping method for Eikonal equations Hongkai Zhao · Mathematics of Computation | 21 May 2004 | 1,145 |
| 32 | Schnelle Multiplikation großer Zahlen Arnold Schönhage, Volker Strassen · Computing | Sep 1971 | 1,111 |
| 33 | Deep Learning with Limited Numerical Precision Suyog Gupta, Ankur Agrawal, Kailash Gopalakrishnan et al. · arXiv (Cornell University) | 9 Feb 2015 | 1,079 |
| 34 | Theano: A CPU and GPU Math Compiler in Python James Bergstra, Olivier Breuleux, Frédéric Bastien et al. · Proceedings of the Python in Science Conferences | 2010 | 1,075 |
| 35 | Theano: new features and speed improvements Frédéric Bastien, Pascal Lamblin, Razvan Pascanu et al. · arXiv (Cornell University) | 23 Nov 2012 | 1,035 |
| 36 | TestU01 Pierre L’Ecuyer, Richard Simard · ACM Transactions on Mathematical Software | 15 Aug 2007 | 1,012 |
| 37 | ACADO toolkit—An open‐source framework for automatic control and dynamic optimization Boris Houska, Hans Joachim Ferreau, Moritz Diehl · Optimal Control Applications and Methods | 26 May 2010 | 997 |
| 38 | Knitro: An Integrated Package for Nonlinear Optimization Richard H. Byrd, Jorge Nocedal, Richard A. Waltz · Nonconvex optimization and its applications | 2006 | 996 |
| 39 | Context-based, adaptive, lossless image coding Xiaolin Wu, Nasir D. Memon · IEEE Transactions on Communications | Apr 1997 | 987 |
| 40 | Mathematical Methods for Digital Computers Anthony Ralston, Herbert S. Wilf, Peter L. Balise · Physics Today | Jul 1961 | 950 |
| 41 | MPFR Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre et al. · ACM Transactions on Mathematical Software | Jun 2007 | 937 |
| 42 | Swinging up a pendulum by energy control Karl Johan Åström, Kazuo Furuta · Automatica | Feb 2000 | 922 |
| 43 | Computing Fourier Transforms and Convolutions on the 2-Sphere James R. Driscoll, D.M. Healy · Advances in Applied Mathematics | Jun 1994 | 891 |
| 44 | A note on Platt’s probabilistic outputs for support vector machines Hsuan-Tien Lin, Chih‐Jen Lin, Ruby C. Weng · Machine Learning | 7 Aug 2007 | 878 |
| 45 | Automatically Tuned Linear Algebra Software R. Clint Whaley, Jack J. Dongarra · Conference on High Performance Computing (Supercomputing) | 7 Nov 1998 | 876 |
| 46 | A unified algebraic approach to linear control design Takao Watanabe · Automatica | 16 Jul 2003 | 873 |
| 47 | Nonlinear programming without a penalty function Roger Fletcher, Sven Leyffer · Mathematical Programming | 2002 | 872 |
| 48 | A survey of CORDIC algorithms for FPGA based computers Ray Andraka | 1998 | 867 |
| 49 | Fundamentals of Matrix Computations. G. W. S., David S. Watkins · Mathematics of Computation | Jul 1992 | 864 |
| 50 | Information-Based Complexity J. F. Traub, H. Wozniakowski · Science | 3 Mar 1989 | 859 |
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.