| 感谢under的hint，偶用google搜的： http://www.caam.rice.edu/~ykzhou/classic-papers.htm －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ The following list is from one of Prof. L.N. Trefethen's seminars, the original post can be found at: seminar on 13 classic papers in numerical analysis I like this list so much. Originally I wanted to put some copies of the papers that I currently have in this webpage, but I don't have right to do so since there would possibly be some copy right issues. If you are in universities, it won't be difficult for you to obtain personal copies from your libraries, the carefully listed citations by Prof. Trefethen provide enough info. (Masters' papers worth serious reading, one reason for me to propagate Prof. Trefethen's posting in this page) I would like to especially quote two interesting comments of Prof. Trefethen and Prof. Higham: We were struck by how young many of the authors were when they wrote these papers (average age: 34), and by how short an influential paper can be (Householder: 3.3 pages, Cooley & Tukey: 4.4). ----L. N. Trefethen It is ironic that with the wealth of facilities we now have for tracking the progress of numerical algorithms (multiple windows in colour, graphical tools, fast printers) we often glean less than Wilkinson and his co-workers did from mere paper tape and lights. ----N. J. Higham (quoted from p. 31 of the book "Accuracy and stability of numerical algorithms" published by SIAM, 1996) ---------------------------------------------------------------------------- From: Nick Trefethen Date: Thu, 6 May 93 10:36:16 -0400 Subject: Classic Papers in Numerical Analysis ---------------------------------------------------------------------------- 1. Cooley & Tukey (1965) the Fast Fourier Transform 2. Courant, Friedrichs & Lewy (1928) finite difference methods for PDE 3. Householder (1958) QR factorization of matrices 4. Curtiss & Hirschfelder (1952) stiffness of ODEs; BD formulas 5. de Boor (1972) calculations with B-splines 6. Courant (1943) finite element methods for PDE 7. Golub & Kahan (1965) the singular value decomposition 8. Brandt (1977) multigrid algorithms 9. Hestenes & Stiefel (1952) the conjugate gradient iteration 10. Fletcher & Powell (1963) optimization via quasi-Newton updates 11. Wanner, Hairer & Norsett (1978) order stars and applications to ODE 12. Karmarkar (1984) interior pt. methods for linear prog. 13. Greengard & Rokhlin (1987) multipole methods for particles [2] Bibliographic citations for 13 "classic papers" 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 73 (1987), 325-348. ^ %----------------------------------------------------------------------------- [3] longer list of papers we considered reading LINEAR ALGEBRA - SYSTEMS OF EQUATIONS AND LEAST-SQUARES Frankel (1950) optimal omega for SOR iteration Hestenes & Stiefel (1952) the conjugate gradient iteration Young (1954) theory of classical iterative methods Householder (1958) QR decomposition Wilkinson (1961) error analysis for systems of eqs. Golub (1965) least-squares problems Strassen (1969) Gaussian elimination is not optimal George (1973) nested dissection Gill, Golub, Murray & Saunders (1974) updating matrix factorizations Concus, Golub & O'Leary (1976) preconditioned conjugate gradients Meijerink & van der Vorst (1977) incomplete LU preconditioning Skeel (1980) iterative refinement and stability Saad & Schultz (1986) GMRES for nonsymmetric systems LINEAR ALGEBRA - EIGENVALUES AND SVD Jacobi (1846) Jacobi's method for matrix eigenvalues Henrici (1958) convergence of the Jacobi method Rutishauser (1958) the LR algorithm Kublanovskaya (1961) the QR algorithm Francis (1961) the QR algorithm Golub & Kahan (1965) computation of the SVD Moler & Stewart (1973) QZ algorithm for gen'd eigenvalues Cuppen (1981) divide and conquer for eigenvalues OPTIMIZATION Dantzig (1951) simplex method for linear programming Davidon (1959) variable metric methods Fletcher & Powell (1963) DFP quasi-Newton update formula Broyden/Fletcher/Goldfarb/Shanno (`70) BFGS quasi-Newton update formula Karmarkar (1984) interior pt methods for linear prog. INTEGRATION Golub & Welsch (1969) Gauss quadrature rules de Boor (1971) adaptive quadrature algorithms APPROXIMATION Remes (1934) Remes algorithm for Chebyshev approx. Schoenberg (1946) splines Powell (1967) near-optimality of Chebyshev interp. Reinsch (1967) smoothing with splines Cox (1972) calculation with B-splines de Boor (1972) calculation with B-splines OTHER Aitken (1932) Aitken extrapolation Cooley & Tukey (1965) the fast Fourier transform Greengard & Rokhlin (1987) fast multipole methods ODEs Curtiss & Hirschfelder (1952) stiffness and BD formulas Dahlquist (1956) stability and convergence Dahlquist (1963) A-stability Butcher (1965) Runge-Kutta methods Gear (1969) stiff ODEs Wanner, Hairer & Norsett (1978) order stars and stability theorems ELLIPTIC PDEs Peaceman & Rachford (1955) ADI Douglas (1955) ADI Strang (1971 or 1973) finite elements and approx. theory Buzbee, Golub & Nielsen (1970) fast Poisson via cyclic reduction Hockney (1965) fast Poisson via FFT Fedorenko (1961) multigrid methods Brandt (1977) multigrid methods PARABOLIC AND HYPERBOLIC PDEs Courant, Friedrichs & Lewy (1928) the CFL condition Crank & Nicolson (1947) finite differences for parabolic PDE O'Brien, Hyman & Kaplan (1951) Von Neumann stability analysis Lax & Richtmyer (1956) general stability theory Lax & Wendroff (1960,1962,1964) methods for solving conservation laws Kreiss (1962) more general stability theory Orszag (1971) spectral methods Kreiss and Oliger (1972) spectral methods Gustafsson, Kreiss & Sundstrom (1972) stability of boundary conditions Chorin (1973) vortex methods for CFD Engquist & Majda (1977) absorbing boundary conditions |
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