[推荐]13篇近代数值分析经典文献.txt
The following list is from one of Prof. L.N. Trefethen';s seminars, theoriginal 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. 31of the book "Accuracy and stability of
numerical algorithms" published by SIAM, 1996)
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From: Nick Trefethen
Date: Thu, 6 May 93 10:36:16 -0400
Subject: Classic Papers in Numerical Analysis
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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
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.
^
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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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