• Topic: Fast Multipole methods
• Paper: Greengard and Rokhlin paper below

On the lighter side of things, here is an interesting paper called "How smart are computers?" By: J. R. Pierce

Suggested Papers:

Cooley & Tukey (1965) Courant, Friedrichs & Lewy (1928) Householder (1958) Curtiss & Hirschfelder (1952) de Boor (1972) Courant (1943) Golub & Kahan (1965) Brandt (1977) Hestenes & Stiefel (1952) Fletcher & Powell (1963) Wanner, Hairer & Norsett (1978) Karmarkar (1984) Greengard & Rokhlin (1987)

the Fast Fourier Transform finite difference methods for PDE QR factorization of matrices stiffness of ODEs; BD formulas calculations with B-splines finite element methods for PDE the singular value decomposition multigrid algorithms the conjugate gradient iteration optimization via quasi-Newton updates order stars and applications to ODE interior pt. methods for linear prog. multipole methods for particles

Nick categorized the 13 papers above into the following three categories:

• Finite algorithms for finite problems: Papers 1, 3, 5
• Infinite algorithms for infinite problems: Papers 2, 4, 6, 7, 10, 11
• Infinite algorithms for finite problems: Papers 8, 9, 12, 13

Full Bibliographic Information:

1. James W. Cooley and John W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Mathematics of Computation 19 (1965), 297-301.


2. R. Courant, K. O. Friedrichs and H. Lewy, "Ueber die partiellen Differenzengleichungen der mathematischen Physik," Mathematische Annalen 100 (1928), 32-74. Translated as: "On the partial difference equations of mathematical physics," IBM Journal of Resarch and Development 11 (1967), 215-234.


3. A. S. Householder, "Unitary triangularization of a nonsymmetric matrix," Journal of the Association of Computing Machinery 5 (1958), 339-342.


4. C. F. Curtiss and J. O. Hirschfelder, "Integration of stiff equations," Proceedings of the National Academy of Sciences 38 (1952), 235-243.


5. C. de Boor, "On calculating with B-splines," Journal of Approximation Theory 6 (1972), 50-62.


6. R. Courant, "Variational methods for the solution of problems of equilibrium and vibrations," Bulletin of the American Mathematical Society 49 (1943), 1-23.


7. G. Golub and W. Kahan, "Calculating the singular values and pseudo-inverse of a matrix," SIAM Journal on Numerical Analysis 2 (1965), 205-224.


8. A. Brandt, "Multi-level adaptive solutions to boundary-value problems," Mathematics of Computation 31 (1977), 333-390.


9. Magnus R. Hestenes and Eduard Stiefel, "Methods of conjugate gradients for solving linear systems," Journal of Research of the National Bureau of Standards 49 (1952), 409-436.


10. R. Fletcher and M. J. D. Powell, "A rapidly convergent descent method for minimization," Computer Journal 6 (1963), 163-168.


11. G. Wanner, E. Hairer and S. P. Norsett, "Order stars and stability theorems," BIT 18 (1974), 475-489.


12. N. Karmarkar, "A new polynomial-time algorithm for linear programming," Combinatorica 4 (1984), 373-395.


13. L. Greengard and V. Rokhlin, "A fast algorithm for particle simulations," Journal of Computational Physics 72 (1987), 325-348.

Other Papers:

Linear Algebra - Eigenvalues and SVD
Jacobi (1846) Henrici (1958) Rutishauser (1958) Kublanovskaya (1961) Francis (1961) Golub & Kahan (1965) Moler & Stewart (1973) Cuppen (1981)	Jacobi's method for matrix eigenvalues convergence of the Jacobi method the LR algorithm the QR algorithm the QR algorithm computation of the SVD QZ algorithm for gen'd eigenvalues divide and conquer for eigenvalues

Optimization
Dantzig (1951) Davidon (1959) Fletcher & Powell (1963) Broyden/Fletcher/Goldfarb/Shanno (`70) Karmarkar (1984)	simplex method for linear programming variable metric methods DFP quasi-Newton update formula BFGS quasi-Newton update formula interior pt methods for linear prog.

Integration
Golub & Welsch (1969) de Boor (1971)	Gauss quadrature rules adaptive quadrature algorithms

Approximation
Remes (1934) Schoenberg (1946) Powell (1967) Reinsch (1967) Cox (1972) de Boor (1972)	Remes algorithm for Chebyshev approx. splines near-optimality of Chebyshev interp. smoothing with splines calculation with B-splines calculation with B-splines

ODEs
Curtiss & Hirschfelder (1952) Dahlquist (1956) Dahlquist (1963) Butcher (1965) Gear (1969) Wanner, Hairer & Norsett (1978)	stiffness and BD formulas stability and convergence A-stability Runge-Kutta methods stiff ODEs order stars and stability theorems

Elliptic PDEs
Peaceman & Rachford (1955) Douglas (1955) Strang (1971 or 1973) Buzbee, Golub & Nielsen (1970) Hockney (1965) Fedorenko (1961) Brandt (1977)	ADI ADI finite elements and approx. theory fast Poisson via cyclic reduction fast Poisson via FFT multigrid methods multigrid methods

Parabolic and Hyperbolic PDEs
Courant, Friedrichs & Lewy (1928) Crank & Nicolson (1947) O'Brien, Hyman & Kaplan (1951) Lax & Richtmyer (1956) Lax & Wendroff (1960,1962,1964) Kreiss (1962) Orszag (1971) Kreiss and Oliger (1972) Gustafsson, Kreiss & Sundstrom (1972) Chorin (1973) Engquist & Majda (1977)	the CFL condition finite differences for parabolic PDE Von Neumann stability analysis general stability theory methods for solving conservation laws more general stability theory spectral methods spectral methods stability of boundary conditions vortex methods for CFD absorbing boundary conditions

Other Notables
Aitken (1932) Cooley & Tukey (1965) Greengard & Rokhlin (1987)	Aitken extrapolation the fast Fourier transform fast multipole methods