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 World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...

. For a fuller history of the subject before this period, see

timeline A timeline is a display of a list of events in chronological order. It is typically a graphic design showing a long bar labelled with dates paralleling it, and usually contemporaneous events. Timelines can use any suitable scale represen ...

and

history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...

1940s

* Monte Carlo simulation (voted one of the top 10

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

s of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis. *

Crank–Nicolson method In numerical analysis, the Crank–Nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differential equations. It is a second-order method in time. It is implicit in time, can be wri ...

was developed by Crank and Nicolson. * Dantzig introduces the simplex method (voted one of the top 10 algorithms of the 20th century) in 1947. * Turing formulated the LU decomposition method.

1950s

Successive over-relaxation In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly convergin ...

was devised simultaneously by D.M. Young, Jr. and by H. Frankel in 1950. * Hestenes, Stiefel, and Lanczos, all from the Institute for Numerical Analysis at the

National Bureau of Standards The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...

, initiate the development of Krylov subspace iteration methods. Voted one of the top 10 algorithms of the 20th century. * ''

Equations of State Calculations by Fast Computing Machines "Equation of State Calculations by Fast Computing Machines" is a scholarly article published by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller in the Journal of Chemical Physics in 1953. ...

'' introduces the

Metropolis–Hastings algorithm In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult. This seq ...

. * In numerical differential equations, Lax and Friedrichs invent the Lax-Friedrichs method. * Householder invents his eponymous matrices and transformation method (voted one of the top 10 algorithms of the 20th century). *

Romberg integration In numerical analysis, Romberg's method is used to estimate the definite integral \int_a^b f(x) \, dx by applying Richardson extrapolation repeatedly on the trapezium rule or the rectangle rule (midpoint rule). The estimates generate a tria ...

* John G.F. Francis and

Vera Kublanovskaya Vera Nikolaevna Kublanovskaya (''née'' Totubalina; November 21, 1920 – February 21, 2012 ) was a Russian mathematician noted for her work on developing computational methods for solving spectral problems of algebra. She proposed the QR algorithm ...

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, to describe the methods of Courant, Hrenikoff, Galerkin and Zienkiewicz, among others. See also here. *Exponential integration by Certaine and Pope. * In computational fluid dynamics and numerical differential equations, Lax and Wendroff invent the Lax-Wendroff method. * Fast Fourier Transform (voted one of the top 10

algorithms In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

of the 20th century) invented by Cooley and Tukey. * First edition of '' Handbook of Mathematical Functions'' by Abramowitz and Stegun, both of the U.S.

. * Broyden does new quasi-Newton method for finding roots in 1965. * The

MacCormack method In computational fluid dynamics, the MacCormack method is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack ...

, for the numerical solution of

hyperbolic partial differential equation In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n-1 derivatives. More precisely, the Cauchy problem can ...

s in computational fluid dynamics, is introduced by MacCormack in 1969. * Verlet (re)discovers a numerical integration algorithm, (first used in 1791 by Delambre, by Cowell and Crommelin in 1909, and by Carl Fredrik Störmer in 1907, hence the alternative names Störmer's method or the Verlet-Störmer method) for dynamics.

1970s

Creation of LINPACK and associated benchmark by Dongarra et al., as well as BLAS.

1980s

* Progress in digital wavelet theory throughout the decade, led by Daubechies et al. *Creation of MINPACK * Fast multipole method (voted one of the top 10

of the 20th century) invented by Rokhlin and Greengard. * First edition of '' Numerical Recipes'' by Press, Teukolsky, et al. * In numerical linear algebra, the

GMRES In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace wi ...

algorithm invented in 1986.

References

External links

The History of Numerical Analysis and Scientific Computing
@ SIAM (Society for Industrial and Applied Mathematics) * {{cite journal , doi = 10.1038/440399a , volume=440 , issue=7083 , title=2020 computing: Milestones in scientific computing , year=2006 , journal=Nature , pages=399–405 , last1 = Ruttimann , first1 = Jacqueline , pmid=16554772, bibcode=2006Natur.440..399R , s2cid=21967804

Monte Carlo Landmark Papers

“Must read” papers in numerical analysis.
Discussion at

MathOverflow MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting merit points for their activities. It is a ...

based upon a selected reading list on Lloyd N. Trefethen'
personal site
nume Numerical analysis