[推荐]13篇近代数值分析经典文献.txt

renwoxing

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
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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

[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.
                                      ^
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[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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