Timeline of scientific computing
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The following is a timeline of scientific computing, also known as computational science.
Before modern computers
18th century
- Simpson rediscovers Simpson's rule, a century after Johannes Kepler (who derived it in 1615 after seeing it used for wine barrels).
- 1733 – The French naturalist Comte de Buffon poses his needle problem.[1][2]
- Euler comes up with a simple numerical method for integrands.[3][4][5]
- c. 500 BCE - Urdhva Tiryakbhyam algorithm, a Vedic method for fast integer multiplication; foundational for Indian mathematics.[6]
- 300 BCE - Babylonian root extraction method, Earliest documented numerical algorithm for square roots.[7]
- c. 250 BCE - Chinese Remainder Theorem Systematic solution to simultaneous congruences; used in cryptography.[8]
19th century
- First formulation of Gram-Schmidt orthogonalisation by Laplace,[9] to be further improved decades later.[10][11][12][13]
- Babbage in 1822, began work on a machine made to compute/calculate values of polynomial functions automatically by using the method of finite differences. This was eventually called the Difference engine.
- Lovelace's note G on the Analytical Engine (1842) describes an algorithm for generating Bernoulli numbers. It is considered the first algorithm ever specifically tailored for implementation on a computer, and thus the first-ever computer programme.[14][15] The engine was never completed, however, so her code was never tested.[16]
- Adams-Bashforth method published.[17]
- In applied mathematics, Jacobi develops technique for solving numerical equations.[18][19][20]
- Gauss Seidel first published.
- To help with computing tides, Harmonic Analyser is built in 1886.
- 850 CE: Al-Kindi's frequency analysis – First systematic cryptanalysis technique for breaking substitution ciphers.[21]
- 1206: Al-Jazari's programmable orchestra – Mechanical automata using pegged cylinders for sequence control (early program storage).[22]
- 1676: Leibniz's chain rule – Foundation for calculus-based optimization later used in backpropagation.[22]
- 1738/1763: Bernoulli's utility theory & Bayes' theorem – Probabilistic frameworks for decision-making algorithms.[22]
1900s (decade)
- 1900 – Runge's work followed by Martin Kutta to invent the Runge-Kutta method for approximating integration for differential equations.[23][24]
1910s (decade)
- 1910 – A-M Cholesky creates a matrix decomposition scheme.[25][26]
- Richardson extrapolation introduced.
1920s
- 1922 – Lewis Fry Richardson introduces numerical weather forecasting by manual calculation, using methods originally developed by Vilhelm Bjerknes as early as 1895.[27][28]
- 1926 – Grete Hermann publishes foundational paper for computer algebra, which established the existence of algorithms (including complexity bounds) for many of the basic problems of abstract algebra, such as ideal membership for polynomial rings.[29]
- 1926 Adams-Moulton method.
- 1927 – Douglas Hartree creates what is later known as the Hartree–Fock method, the first ab initio quantum chemistry methods. However, manual solutions of the Hartree–Fock equations for a medium-sized atom were laborious and small molecules required computational resources far beyond what was available before 1950.
- 1928 – Leslie Comrie proposes using commercial tabulating machines to perform scientific calculations, and himself uses them to expand Ernest William Brown's lunar calculations.
1930s
This decade marks the first major strides to a modern computer, and hence the start of the modern era.
- Fermi's Rome physics research group (informal name I ragazzi di Via Panisperna) develop statistical algorithms based on Comte de Buffon's work, that would later become the foundation of the Monte Carlo method. See also FERMIAC.
- Shannon explains how to use electric circuits to do Boolean algebra in "A Symbolic Analysis of Relay and Switching Circuits"
- John Vincent Atanasoff and Clifford Berry create the first electronic non-programmable, digital computing device, the Atanasoff–Berry Computer, from 1937-42.
- Complex number calculator created by Stibitz.
- At Columbia University's Rutherford Laboratory Wallace J. Eckert uses commercial tabulating machinery from IBM, some of it specially modified, for scientific computation.
1940s
- 1947 – Metropolis algorithm for Monte Carlo simulation (named one of the top-10 algorithms of the 20th century)[30] invented at Los Alamos by von Neumann, Ulam and Metropolis.[31][32][33]
- George Dantzig introduces the simplex method (named one of the top 10 algorithms of the 20th century)[30] in 1947.[34]
- Ulam and von Neumann introduce the notion of cellular automata.[35]
- Turing formulated the LU decomposition method.[36]
- A. W. H. Phillips invents the MONIAC hydraulic computer at LSE, better known as "Phillips Hydraulic Computer".[37][38]
- First hydro simulations occurred at Los Alamos.[39][40]
1950s
- First successful weather predictions on a computer occurred.[41][42]
- Hestenes, Stiefel, and Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods.[43][44][45][46] Named one of the top 10 algorithms of the 20th century.[30]
- Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm.[47]
- Molecular dynamics invented by Bernie Alder and Wainwright [48][49]
- A S Householder invents his eponymous matrices and transformation method (voted one of the top 10 algorithms of the 20th century).[50]
- 1953 – Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou discover the Fermi–Pasta–Ulam–Tsingou problem through computer simulations of a vibrating string.[51]
- A team led by John Backus develops the FORTRAN compiler and programming language at IBM's research centre in San Jose, California. This sped the adoption of scientific programming,[52][53][54] and is one of the oldest extant programming languages, as well as one of the most popular in science and engineering.
1960s
- 1960 – First recorded use of the term "finite element method" by Ray Clough to describe the earlier methods of Richard Courant, Alexander Hrennikoff and Olgierd Zienkiewicz in structural analysis.[55]
- 1961 – John G.F. Francis[56][57] and Vera Kublanovskaya[58] invent QR factorization (voted one of the top 10 algorithms of the 20th century).
- 1963 – Edward Lorenz discovers the butterfly effect on a computer, attracting interest in chaos theory.[59]
- 1961 – Using computational investigations of the 3-body problem, Michael Minovitch formulates the gravity assist method.[60][61]
- 1964 – Molecular dynamics invented independently by Aneesur Rahman.[62]
- 1965 – fast Fourier transform developed by James W. Cooley and John W. Tukey.[63]
- 1964 – Walter Kohn, with Lu Jeu Sham and Pierre Hohenberg, instigates the development of density functional theory,[64][65] for which he shares the 1998 Nobel Chemistry Prize with John Pople.[66] This contribution is arguably the earliest work to which Nobels were given for a computer program or computational technique.
- First regression calculations in economics.
1970s
- 1975 – Benoit Mandelbrot coins the term "fractal" to describe the self-similarity found in the Fatou, Julia and Mandelbrot sets. Fractals become the first mathematical visualization tool extensively explored with computing.[67]
- 1977 – Kenneth Appel and Wolfgang Haken prove the four colour theorem, the first theorem to be proved by computer.[68][69][70]
1980s
- Fast multipole method (voted one of the top 10 algorithms of the 20th century) invented by Vladimir Rokhlin and Leslie Greengard.[71][72][73]
- Car–Parrinello molecular dynamics developed by Roberto Car and Michele Parrinello
1990s
- 1990 – In computational genomics and sequence analysis, the Human Genome Project, an endeavour to sequence the entire human genome, begins.
- 1998 – Kepler conjecture is almost all but certainly proved algorithmically by Thomas Hales.
- The appearance of the first research grids using volunteer computing – GIMPS (1996), distributed.net (1997) and Seti@Home (1999).
2000s
- 2000 – The Human Genome Project completes a rough draft of human genome.
- 2003 – The Human Genome Project completed.
- 2002 – The BOINC architecture is launched.
2010s
- Foldit players solve virus structure, one of the first cases of a game solving a scientific question.
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See also
- Computational science
- History of computing
- History of mathematics
- Timeline of mathematics
- Timeline of algorithms
- Timeline of computational physics
- Timeline of computational mathematics
- Timeline of numerical analysis after 1945
- History of computing hardware
References
Page Template:Reflist/styles.css has no content.
- ^ Buffon, G. Editor's note concerning a lecture given 1733 by Mr. Le Clerc de Buffon to the Royal Academy of Sciences in Paris. Histoire de l'Acad. Roy. des Sci., pp. 43-45, 1733; according to Weisstein, Eric W. "Buffon's Needle Problem." From MathWorld--A Wolfram Web Resource. 20 Dec 2012 20 Dec 2012.
- ^ Buffon, G. "Essai d'arithmétique morale." Histoire naturelle, générale er particulière, Supplément 4, 46-123, 1777; according to Weisstein, Eric W. "Buffon's Needle Problem." From MathWorld--A Wolfram Web Resource. 20 Dec 2012
- ^ Euler, L. Institutionum calculi integralis. Impensis Academiae Imperialis Scientiarum, 1768.
- ^ Butcher, John C. (2003), Numerical Methods for Ordinary Differential Equations, New York: John Wiley & Sons, Template:ISBN.
- ^ Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems, Berlin, New York: Springer-Verlag, Template:ISBN.
- ^ Page Module:Citation/CS1/styles.css has no content.The Rig-Vedic and Post-Rig-Vedic Polity (1500 BCE-500 BCE) [PDF, E-Book]. Vernon Press. 2020. doi:10.54094/b-b5e8c492cc. ISBN 978-1-64889-001-7.
- ^ Page Module:Citation/CS1/styles.css has no content."Timeline of algorithms", Wikipedia, 2025-05-13, retrieved 2025-07-12
- ^ Page Module:Citation/CS1/styles.css has no content."History of Algorithms". www.enjoyalgorithms.com. Retrieved 2025-07-12.
- ^ Laplace, PS. (1816). Théorie Analytique des Probabilités :First Supplement, p. 497ff.
- ^ Page Module:Citation/CS1/styles.css has no content.Gram, J. P. (1883). "Ueber die Entwickelung reeler Funtionen in Reihen mittelst der Methode der kleinsten Quadrate". Journal für die reine und angewandte MathematikJournal für die reine und angewandte Mathematik. 94: 71–73.
- ^ Page Module:Citation/CS1/styles.css has no content.Schmidt, E. "Zur Theorie der linearen und nichtlinearen Integralgleichungen. I. Teil: Entwicklung willkürlicher Funktionen nach Systemen vorgeschriebener". Math. Ann. 63: 1907.
- ^ Earliest Known Uses of Some of the Words of Mathematics (G). As of Aug 2017.
- ^ Page Module:Citation/CS1/styles.css has no content.Farebrother, RW (1988). Linear Least Squares Computations. CRC Press. ISBN 9780824776619. Retrieved 19 August 2017.
- ^ Page Module:Citation/CS1/styles.css has no content.Simonite, Tom (24 March 2009). "Short Sharp Science: Celebrating Ada Lovelace: the 'world's first programmer'". New Scientist. Retrieved 14 April 2012.
- ^ Tom Stoppard's “Arcadia,” at Twenty. By Brad Leithauser. The New Yorker, August 8, 2013.
- ^ Page Module:Citation/CS1/styles.css has no content.Kim, Eugene Eric; Toole, Betty Alexandra (May 1999). "Ada and the first computer". Scientific American. 280 (5): 70–71. Bibcode:1999SciAm.280e..76E. doi:10.1038/scientificamerican0599-76.
- ^ Bashforth, Francis (1883), An Attempt to test the Theories of Capillary Action by comparing the theoretical and measured forms of drops of fluid. With an explanation of the method of integration employed in constructing the tables which give the theoretical forms of such drops, by J. C. Adams, Cambridge.
- ^ Jacobi's Ideas on Eigenvalue Computation in a modern context, Henk van der Vorst.
- ^ Jacobi method, Encyclopedia of Mathematics.
- ^ The Early History of Matrix Iterations: With a Focus on the Italian Contribution, Michele Benzi, 26 October 2009. SIAM Conference on Applied Linear Algebra, Monterey Bay – Seaside, California.
- ^ Page Module:Citation/CS1/styles.css has no content."History of Algorithms". www.enjoyalgorithms.com. Retrieved 2025-07-12.
- ^ a b c Page Module:Citation/CS1/styles.css has no content."Timeline of artificial intelligence", Wikipedia, 2025-07-12, retrieved 2025-07-12
- ^ MW Kutta. "Beiträge zur näherungsweisen Integration totaler Differentialgleichungen" [Contributions to the approximate integration of total differential equations] (in German). Thesis, University of Munich.
- 1901 – Page Module:Citation/CS1/styles.css has no content."Reprinted", Z. Math. Phys., 46: 435–453, 1901 and in B.G Teubner, 1901.
- ^ Runge, C., "Über die numerische Auflösung von Differentialgleichungen" [About the numerical solution of differential equations](in German), Math. Ann. 46 (1895) 167-178.
- ^ Page Module:Citation/CS1/styles.css has no content.Commandant Benoit (1924). "Note sur une méthode de résolution des équations normales provenant de l'application de la méthode des moindres carrés à un système d'équations linéaires en nombre inférieur à celui des inconnues (Procédé du Commandant Cholesky)". Bulletin Géodésique. 2: 67–77. doi:10.1007/BF03031308.
- ^ Page Module:Citation/CS1/styles.css has no content.Cholesky (1910). Sur la résolution numérique des systèmes d'équations linéaires.
- ^ L F Richardson, Weather Prediction by Numerical Process. Cambridge University Press (1922).
- ^ Page Module:Citation/CS1/styles.css has no content.Lynch, Peter (March 2008). "The origins of computer weather prediction and climate modeling" (PDF). Journal of Computational Physics. 227 (7). University of Miami: 3431–44. Bibcode:2008JCoPh.227.3431L. doi:10.1016/j.jcp.2007.02.034. Archived from the original (PDF) on 2010-07-08. Retrieved 2010-12-23.
- ^ Page Module:Citation/CS1/styles.css has no content.Grete Hermann (1926). "Die Frage der endlich vielen Schritte in der Theorie der Polynomideale". Mathematische Annalen. 95: 736–788. doi:10.1007/bf01206635. S2CID 115897210. Archived from the original on 2016-10-09. Retrieved 2017-05-05.
- ^ a b c Page Module:Citation/CS1/styles.css has no content.Dongarra, J.; Sullivan, F. (January 2000). "Guest Editors Introduction: the Top 10 Algorithms". Computing in Science & Engineering. 2 (1): 22–23. Bibcode:2000CSE.....2a..22D. doi:10.1109/MCISE.2000.814652. ISSN 1521-9615.
- ^ Page Module:Citation/CS1/styles.css has no content.Metropolis, N. (1987). "The Beginning of the Monte Carlo method" (PDF). Los Alamos Science. 15: 125.. Accessed 5 May 2012.
- ^ S. Ulam, R. D. Richtmyer, and J. von Neumann(1947). Statistical methods in neutron diffusion. Los Alamos Scientific Laboratory report LAMS–551.
- ^ Page Module:Citation/CS1/styles.css has no content.Metropolis, N.; Ulam, S. (1949). "The Monte Carlo method". Journal of the American Statistical Association. 44 (247): 335–341. doi:10.1080/01621459.1949.10483310. PMID 18139350.
- ^ Page Module:Citation/CS1/styles.css has no content."SIAM News, November 1994". Archived from the original on 16 April 2009. Retrieved 6 June 2012. Systems Optimization Laboratory, Stanford University Huang Engineering Center (site host/mirror).
- ^ Von Neumann, J., Theory of Self-Reproducing Automata, Univ. of Illinois Press, Urbana, 1966.
- ^ A. M. Turing, Rounding-off errors in matrix processes. Quart. J Mech. Appl. Math. 1 (1948), 287–308 (according to Poole, David (2006), Linear Algebra: A Modern Introduction (2nd ed.), Canada: Thomson Brooks/Cole, Template:ISBN.) .
- ^ The computer model that once explained the British economy. Larry Elliott, The Guardian, Thursday 8 May 2008.
- ^ Phillip's Economic Computer, 1949. Script error: No such module "webarchive". Exhibit at London Science Museum.
- ^ Richtmyer, R. D. (1948). Proposed Numerical Method for Calculation of Shocks. Los Alamos, NM: Los Alamos Scientific Laboratory LA-671.
- ^ Page Module:Citation/CS1/styles.css has no content.Von Neumann, J.; Richtmyer, R. D. (1950). "A Method for the Numerical Calculation of Hydrodynamic Shocks". Journal of Applied Physics. 21 (3): 232–237. Bibcode:1950JAP....21..232V. doi:10.1063/1.1699639.
- ^ Page Module:Citation/CS1/styles.css has no content.Charney, J.; Fjørtoft, R.; von Neumann, J. (1950). "Numerical Integration of the Barotropic Vorticity Equation". Tellus. 2 (4): 237–254. Bibcode:1950Tell....2..237C. doi:10.1111/j.2153-3490.1950.tb00336.x (inactive 11 December 2025).
{{cite journal}}: CS1 maint: DOI inactive as of December 2025 (link) - ^ See the review article:- Page Module:Citation/CS1/styles.css has no content.Smagorinsky, J (1983). "The Beginnings of Numerical Weather Prediction and General Circulation Modelling: Early Recollections" (PDF). Advances in Geophysics. 25: 3–37. Bibcode:1983AdGeo..25....3S. doi:10.1016/S0065-2687(08)60170-3. ISBN 9780120188253. Retrieved 6 June 2012.
- ^ Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems, J. Res. Natl. Bur. Stand. 49, 409-436 (1952).
- ^ Eduard Stiefel, U¨ ber einige Methoden der Relaxationsrechnung (in German), Z. Angew. Math. Phys. 3, 1-33 (1952).
- ^ Cornelius Lanczos, Solution of Systems of Linear Equations by Minimized Iterations, J. Res. Natl. Bur. Stand. 49, 33-53 (1952).
- ^ Cornelius Lanczos, An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators, J. Res. Natl. Bur. Stand. 45, 255-282 (1950).
- ^ Page Module:Citation/CS1/styles.css has no content.Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E. (1953). "Equations of State Calculations by Fast Computing Machines" (PDF). Journal of Chemical Physics. 21 (6): 1087–1092. Bibcode:1953JChPh..21.1087M. doi:10.1063/1.1699114. OSTI 4390578. S2CID 1046577.
- ^ Page Module:Citation/CS1/styles.css has no content.Alder, B. J.; Wainwright, T. E. (1957). "Phase Transition for a Hard Sphere System". J. Chem. Phys. 27 (5): 1208. Bibcode:1957JChPh..27.1208A. doi:10.1063/1.1743957. S2CID 10791650.
- ^ Page Module:Citation/CS1/styles.css has no content.Alder, B. J.; Wainwright, T. E. (1962). "Phase Transition in Elastic Disks". Phys. Rev. 127 (2): 359–361. Bibcode:1962PhRv..127..359A. doi:10.1103/PhysRev.127.359. OSTI 4798469.
- ^ Page Module:Citation/CS1/styles.css has no content.Householder, A. S. (1958). "Unitary Triangularization of a Nonsymmetric Matrix" (PDF). Journal of the ACM. 5 (4): 339–342. doi:10.1145/320941.320947. MR 0111128. S2CID 9858625.
- ^ Fermi, E. (posthumously); Pasta, J.; Ulam, S. (1955) : Studies of Nonlinear Problems (accessed 25 Sep 2012). Los Alamos Laboratory Document LA-1940. Also appeared in 'Collected Works of Enrico Fermi', E. Segre ed., University of Chicago Press, Vol.II,978–988,1965. Recovered 21 Dec 2012
- ^ W.W. McDowell Award citation: Page Module:Citation/CS1/styles.css has no content."W. Wallace McDowell Award". Archived from the original on September 29, 2007. Retrieved April 15, 2008.
- ^ National Medal of Science citation: Page Module:Citation/CS1/styles.css has no content."The President's National Medal of Science: John Backus". National Science Foundation. Retrieved March 21, 2007.
- ^ Page Module:Citation/CS1/styles.css has no content."ACM Turing Award Citation: John Backus". Association for Computing Machinery. Archived from the original on February 4, 2007. Retrieved March 22, 2007.
- ^ RW Clough, "The Finite Element Method in Plane Stress Analysis," Proceedings of 2nd ASCE Conference on Electronic Computation, Pittsburgh, PA, Sept. 8, 9, 1960.
- ^ Page Module:Citation/CS1/styles.css has no content.Francis, J.G.F. (1961). "The QR Transformation, I". The Computer Journal. 4 (3): 265–271. doi:10.1093/comjnl/4.3.265.
- ^ Page Module:Citation/CS1/styles.css has no content.Francis, J.G.F. (1962). "The QR Transformation, II". The Computer Journal. 4 (4): 332–345. doi:10.1093/comjnl/4.4.332.
- ^ Page Module:Citation/CS1/styles.css has no content.Kublanovskaya, Vera N. (1961). "On some algorithms for the solution of the complete eigenvalue problem". USSR Computational Mathematics and Mathematical Physics. 1 (3): 637–657. doi:10.1016/0041-5553(63)90168-X. Also published in: Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki [Journal of Computational Mathematics and Mathematical Physics], 1(4), pages 555–570 (1961).
- ^ Page Module:Citation/CS1/styles.css has no content.Lorenz, Edward N. (1963). "Deterministic Nonperiodic Flow" (PDF). Journal of the Atmospheric Sciences. 20 (2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2.
- ^ Minovitch, Michael: "A method for determining interplanetary free-fall reconnaissance trajectories," Jet Propulsion Laboratory Technical Memo TM-312-130, pages 38-44 (23 August 1961).
- ^ Christopher Riley and Dallas Campbell, Oct 22, 2012. "The maths that made Voyager possible". BBC News Science and Environment. Recovered 16 Jun 2013.
- ^ Page Module:Citation/CS1/styles.css has no content.Rahman, A (1964). "Correlations in the Motion of Atoms in Liquid Argon". Phys Rev. 136 (2A): A405–A41. Bibcode:1964PhRv..136..405R. doi:10.1103/PhysRev.136.A405.
- ^ Page Module:Citation/CS1/styles.css has no content.Cooley, James W.; Tukey, John W. (1965). "An algorithm for the machine calculation of complex Fourier series" (PDF). Math. Comput. 19 (90): 297–301. Bibcode:1965MaCom..19..297C. doi:10.1090/s0025-5718-1965-0178586-1.[permanent dead link]
- ^ Page Module:Citation/CS1/styles.css has no content.Kohn, Walter; Hohenberg, Pierre (1964). "Inhomogeneous Electron Gas". Physical Review. 136 (3B): B864–B871. Bibcode:1964PhRv..136..864H. doi:10.1103/PhysRev.136.B864.
- ^ Page Module:Citation/CS1/styles.css has no content.Kohn, Walter; Sham, Lu Jeu (1965). "Self-Consistent Equations Including Exchange and Correlation Effects". Physical Review. 140 (4A): A1133–A1138. Bibcode:1965PhRv..140.1133K. doi:10.1103/PHYSREV.140.A1133.
- ^ Page Module:Citation/CS1/styles.css has no content."The Nobel Prize in Chemistry 1998". Nobelprize.org. Retrieved 2008-10-06.
- ^ B. Mandelbrot; Les objets fractals, forme, hasard et dimension (in French). Publisher: Flammarion (1975), Template:ISBN; English translation Fractals: Form, Chance and Dimension. Publisher: Freeman, W. H & Company. (1977). Template:ISBN.
- ^ Page Module:Citation/CS1/styles.css has no content.Appel, Kenneth; Haken, Wolfgang (1977). "Every planar map is four colorable, Part I: Discharging". Illinois Journal of Mathematics. 21 (3): 429–490. doi:10.1215/ijm/1256049011.
- ^ Page Module:Citation/CS1/styles.css has no content.Appel, K.; Haken, W. (1977). "Every Planar Map is Four-Colorable, II: Reducibility". Illinois J. Math. 21: 491–567. doi:10.1215/ijm/1256049012.
- ^ Page Module:Citation/CS1/styles.css has no content.Appel, K.; Haken, W. (1977). "The Solution of the Four-Color Map Problem". Sci. Am. 237 (4): 108–121. Bibcode:1977SciAm.237d.108A. doi:10.1038/scientificamerican1077-108.
- ^ L. Greengard, The Rapid Evaluation of Potential Fields in Particle Systems, MIT, Cambridge, (1987).
- ^ Rokhlin, Vladimir (1985). "Rapid Solution of Integral Equations of Classic Potential Theory." J. Computational Physics Vol. 60, pp. 187-207.
- ^ Page Module:Citation/CS1/styles.css has no content.Greengard, L.; Rokhlin, V. (1987). "A fast algorithm for particle simulations". J. Comput. Phys. 73 (2): 325–348. Bibcode:1987JCoPh..73..325G. doi:10.1016/0021-9991(87)90140-9.
External links
- SIAM (Society for Industrial and Applied Mathematics) News. Top 10 Algorithms of the 20th Century.
- The History of Numerical Analysis and Scientific Computing @ SIAM (Society for Industrial and Applied Mathematics)
- Page Module:Citation/CS1/styles.css has no content.Ruttimann, Jacqueline (2006). "2020 computing: Milestones in scientific computing". Nature. 440 (7083): 399–405. Bibcode:2006Natur.440..399R. doi:10.1038/440399a. PMID 16554772. S2CID 21967804.
- Page Module:Citation/CS1/styles.css has no content.Anderson, H. L. (1986). "Scientific Uses of the MANIAC". Journal of Statistical Physics. 43 (5–6): 731–748. Bibcode:1986JSP....43..731A. doi:10.1007/BF02628301. S2CID 122676398.
- IEEE Milestones
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