Timeline of numerical analysis after 1945

The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of mathematics.

1940s

Monte Carlo simulation (voted one of the top 10 algorithms of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis.^[1]^[2]^[3]
Crank–Nicolson method was developed by Crank and Nicolson.^[4]
Dantzig introduces the simplex method (voted one of the top 10 algorithms of the 20th century) in 1947.^[5]
Turing formulated the LU decomposition method.^[6]

1950s

Successive over-relaxation was devised simultaneously by D.M. Young, Jr.^[7] and by H. Frankel in 1950.
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.^[8]^[9]^[10]^[11] Voted one of the top 10 algorithms of the 20th century.
Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm.^[12]
Householder invents his eponymous matrices and transformation method (voted one of the top 10 algorithms of the 20th century).^[13]
John G.F. Francis^[14] and Vera Kublanovskaya^[15] invent QR factorization (voted one of the top 10 algorithms of the 20th century).

1960s

First recorded use of the term "finite element method" by Ray Clough,^[16] to describe the methods of Courant, Hrenikoff, Galerkin and Zienkiewicz, among others. See also here.
In computational fluid dynamics and numerical differential equations, Lax and Wendroff invent the Lax-Wendroff method.^[17]
Fast Fourier Transform (voted one of the top 10 algorithms of the 20th century) invented by Cooley and Tukey.^[18]
First edition of Handbook of Mathematical Functions by Abramowitz and Stegun, both of the U.S.National Bureau of Standards.^[19]
The MacCormack method, for the numerical solution of hyperbolic partial differential equations in computational fluid dynamics, is introduced by MacCormack in 1969.^[20]

1980s

Fast multipole method (voted one of the top 10 algorithms of the 20th century) invented by Rokhlin and Greengard.^[21]^[22]^[23]
First edition of Numerical Recipes by Press, Teukolsky, et al.^[24]

References

B. Cipra (2000), Top 10 Algorithms of the 20th Century. SIAM (Society for Industrial and Applied Mathematics) News. Accessed Dec 2012.

^ Metropolis, N. (1987). "The Beginning of the Monte Carlo method" (PDF). Los Alamos Science. No. 15, Page 125. {{cite journal}}: |volume= has extra text (help). 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.
^ N. Metropolis and S. Ulam (1949). The Monte Carlo method. Journal of the American Statistical Association 44:335–341.
^ Crank, J. (John); Nicolson, P. (Phyllis) (1947). "A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type". Proc. Camb. Phil. Soc. 43 (1): 50–67. doi:10.1007/BF02127704. Retrieved 17 October 2013. {{cite journal}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
^ "SIAM News, November 1994". Retrieved 6 June 2012. Hosted at Systems Optimization Laboratory, Stanford University, Huang Engineering Center.
^ 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, ISBN 0-534-99845-3.) .
^ Young, David M. (1 May 1950), Iterative methods for solving partial difference equations of elliptical type (PDF), PhD thesis, Harvard University, retrieved 15 June 2009
^ 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).
^ Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E. (1953): Equations of State Calculations by Fast Computing Machines (Retrieved 3 May 2012). Journal of Chemical Physics 21 (6): 1087–1092. Bibcode 1953JChPh..21.1087M. doi:10.1063/1.1699114.
^ Householder, A. S. (1958). "Unitary Triangularization of a Nonsymmetric Matrix". Journal of the ACM. 5 (4): 339–342. doi:10.1145/320941.320947. MR 0111128.
^ J.G.F. Francis, "The QR Transformation, I", The Computer Journal, 4(3), pages 265–271 (1961, received October 1959) online at oxfordjournals.org;J.G.F. Francis, "The QR Transformation, II" The Computer Journal, 4(4), pages 332–345 (1962) online at oxfordjournals.org.
^ Vera N. Kublanovskaya (1961), "On some algorithms for the solution of the complete eigenvalue problem," USSR Computational Mathematics and Mathematical Physics, 1(3), pages 637–657 (1963, received Feb 1961). Also published in: Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki [Journal of Computational Mathematics and Mathematical Physics], 1(4), pages 555–570 (1961).
^ RW Clough, “The Finite Element Method in Plane Stress Analysis,” Proceedings of 2nd ASCE Conference on Electronic Computation, Pittsburgh, PA, Sept. 8, 9, 1960.
^ P.D Lax; B. Wendroff (1960). "Systems of conservation laws". Commun. Pure Appl Math. 13 (2): 217–237. doi:10.1002/cpa.3160130205.
^ Cooley, James W., and John W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput. 19, 297–301 (1965).
^ M Abramowitz and I Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Publisher: Dover Publications. Publication date: 1964; ISBN 0-486-61272-4;OCLC Number:18003605 .
^ MacCormack, R. W., The Effect of viscosity in hypervelocity impact cratering, AIAA Paper, 69-354 (1969).
^ 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.
^ L. Greengard and V. Rokhlin, "A fast algorithm for particle simulations," J. Comput. Phys., 73 (1987), no. 2, pp. 325–348.
^ Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (1986). Numerical Recipes: The Art of Scientific Computing. New York: Cambridge University Press. ISBN 0-521-30811-9.

External links

The History of Numerical Analysis and Scientific Computing @ SIAM (Society for Industrial and Applied Mathematics)
Jacqueline Ruttimann. 2020 computing: Milestones in scientific computing (HTML document) and (PDF link). Nature 440, 399–405 (23 March 2006) | doi:10.1038/440399a. Nature.com news feature; recovered 20 Oct 2012.
The Monte Carlo Method: Classic Papers
Monte Carlo Landmark Papers
“Must read” papers in numerical analysis. Discussion at Math Overflow based upon a selected reading list on Lloyd N. Trefethen's personal site.

[1] Metropolis, N. (1987). "The Beginning of the Monte Carlo method" (PDF). Los Alamos Science. No. 15, Page 125. {{cite journal}}: |volume= has extra text (help). Accessed 5 may 2012.

[2] S. Ulam, R. D. Richtmyer, and J. von Neumann(1947). Statistical methods in neutron diffusion. Los Alamos Scientific Laboratory report LAMS–551.

[3] N. Metropolis and S. Ulam (1949). The Monte Carlo method. Journal of the American Statistical Association 44:335–341.

[4] Crank, J. (John); Nicolson, P. (Phyllis) (1947). "A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type". Proc. Camb. Phil. Soc. 43 (1): 50–67. doi:10.1007/BF02127704. Retrieved 17 October 2013. {{cite journal}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)

[5] "SIAM News, November 1994". Retrieved 6 June 2012. Hosted at Systems Optimization Laboratory, Stanford University, Huang Engineering Center.

[6] 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, ISBN 0-534-99845-3.) .

[7] Young, David M. (1 May 1950), Iterative methods for solving partial difference equations of elliptical type (PDF), PhD thesis, Harvard University, retrieved 15 June 2009

[8] Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems, J. Res. Natl. Bur. Stand. 49, 409–436 (1952).

[9] Eduard Stiefel,U¨ ber einige Methoden der Relaxationsrechnung (in German), Z. Angew. Math. Phys. 3, 1–33 (1952).

[10] Cornelius Lanczos, Solution of Systems of Linear Equations by Minimized Iterations, J. Res. Natl. Bur. Stand. 49, 33–53 (1952).

[11] 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).

[12] Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E. (1953): Equations of State Calculations by Fast Computing Machines (Retrieved 3 May 2012). Journal of Chemical Physics 21 (6): 1087–1092. Bibcode 1953JChPh..21.1087M. doi:10.1063/1.1699114.

[13] Householder, A. S. (1958). "Unitary Triangularization of a Nonsymmetric Matrix". Journal of the ACM. 5 (4): 339–342. doi:10.1145/320941.320947. MR 0111128.

[14] J.G.F. Francis, "The QR Transformation, I", The Computer Journal, 4(3), pages 265–271 (1961, received October 1959) online at oxfordjournals.org;J.G.F. Francis, "The QR Transformation, II" The Computer Journal, 4(4), pages 332–345 (1962) online at oxfordjournals.org.

[15] Vera N. Kublanovskaya (1961), "On some algorithms for the solution of the complete eigenvalue problem," USSR Computational Mathematics and Mathematical Physics, 1(3), pages 637–657 (1963, received Feb 1961). Also published in: Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki [Journal of Computational Mathematics and Mathematical Physics], 1(4), pages 555–570 (1961).

[16] RW Clough, “The Finite Element Method in Plane Stress Analysis,” Proceedings of 2nd ASCE Conference on Electronic Computation, Pittsburgh, PA, Sept. 8, 9, 1960.

[17] P.D Lax; B. Wendroff (1960). "Systems of conservation laws". Commun. Pure Appl Math. 13 (2): 217–237. doi:10.1002/cpa.3160130205.

[18] Cooley, James W., and John W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput. 19, 297–301 (1965).

[19] M Abramowitz and I Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Publisher: Dover Publications. Publication date: 1964; ISBN 0-486-61272-4;OCLC Number:18003605 .

[20] MacCormack, R. W., The Effect of viscosity in hypervelocity impact cratering, AIAA Paper, 69-354 (1969).

[21] L. Greengard, The Rapid Evaluation of Potential Fields in Particle Systems, MIT, Cambridge, (1987).

[22] Rokhlin, Vladimir (1985). "Rapid Solution of Integral Equations of Classic Potential Theory." J. Computational Physics Vol. 60, pp. 187–207.

[23] L. Greengard and V. Rokhlin, "A fast algorithm for particle simulations," J. Comput. Phys., 73 (1987), no. 2, pp. 325–348.

[24] Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (1986). Numerical Recipes: The Art of Scientific Computing. New York: Cambridge University Press. ISBN 0-521-30811-9.

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