“Must read” papers in numerical analysis
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In 1993, Prof. L.N. Trefethen published a NA-net posting with a list of thirteen paper he used for teaching the seminar Classic Papers in Numerical Analysis. In Trefethen's words, ... this course provided a satisfying vison of the broad scope of numerical analysis and the sense of excitement at what a diversity of beautiful and powerful ideas have been invented in this field. Prof. Trefethen's list (links):
Most readers of this note, according Prof. Trefethen, will have thought of other classic authors and papers that should have been on the list.
na.numerical-analysis reference-request soft-question big-list
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11 Answers
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J. von Neumann, H.H. Goldstine, Numerical Inverting of Matrices of High Order, Bull. Amer. Math. Soc., Vol. 53, No. 11, pp. 1021-1099, 1947. According to J. Grcar, Birthday of Modern Numerical Analysis, available here or here, this paper is considered the first paper in modern analysis because it is the first to study rounding error and because much of the paper is an essay on scientific computing (albeit with an emphasis on numerical linear algebra).
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Metropolis N, Ulam S (1949) The Monte Carlo method J. Am. Stat. Assoc. 44:335-341 Marsaglia G (1968) Random numbers fall mainly in the planes. Proc. Natl. Acad. Sci. USA 61:25-28
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Fermi, Pasta, Ulam, Studies of Nonlinear Problems, unpublished report from Los Alamos National Laboratory, 1955. This paper arguably started the numerical investigation of nonlinear dynamics and chaos, which has become a huge field. See for example Ford, The Fermi-Pasta-Ulam problem: Paradox turns discovery, Physics Reports 213 (2002) pp. 271-310 for a review.
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P. D. Lax & B. Wendroff. On the stability of difference schemes, Communications on Pure and Applied Mathematics 15, pp 363–371 (1962).
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J. Crank and P. Nicolson (1947) A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Mathematical Proceedings of the Cambridge Philosophical Society 43, pp. 50-67
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S.K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Matematicheskii Sbornik (1959). (in Russian) Virtually all modern methods for nonlinear hyperbolic PDEs are based on this.
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Edward N. Lorenz (1963). "Deterministic Nonperiodic Flow". Journal of the Atmospheric Sciences 20 (2): 130–141. This demonstrated the butterfly effect.
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Jinchao Xu, Iterative methods by space decomposition and subspace correction, SIAM Review 34(4):581-613, 1992.
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L.F. Richardson, The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam, Proceedings of the Royal Society of London, 1910, available here. From the Abstract,
According CFD-Online, this 50 page paper is a key paper in Computational Fluid Dynamics.
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Any mention of de Boor should also include Jos Stam's work: www.dgp.toronto.edu/~stam/reality/Research/pub.html (Especially his siggraph 1999 course notes, which cover a number of useful approaches for dealing with b-splines.)
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