Workshop


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Survey and Review

Preconditioners for Krylov subspace methods: An overview J. W. Pearson and J. Pestana, GAMM-Mitteilungen (2020)
Algebraic multigrid methods， J. C. Xu and L. Zikatanov, Acta Numerica (2017), 591--721.
Randomized algorithms in numerical linear algebra， R. Kannan and S. Vempala, Acta Numerica (2017), 95--125.
A survey of direct methods for sparse linear systems, T. A. Davis, S. Rajamanickam and W. M. Sid-Lakhdar, Acta Numerica (2016), 383--566.
Preconditioning, A. J. Wathen, Acta Numerica (2015), 329--376.
Motivations and realizations of Krylov subspace methods for large sparse linear systems, Bai, JCAM, 2015
Recent computational developments in Krylov subspace methods for linear systems, Simoncini and Szyld, NLAA, 2007
Numerical solution of saddle point problems, Benzi, Golub and Liesen, Acta Numerica, 2005
Preconditioning Techniques for Large Linear Systems: A Survey, Benzi, JCP, 2002
Iterative solution of linear systems in the 20th century, Saad and van der Vorst, JCAM, 123(2000), 1-33
Eigenvalue computation in the 20th century, Golub and van der Vorst, JCAM, 123(2000), 35-65

General Theory

On the numerical behavior of matrix splitting iteration methods for solving linear systems, Z.-Z. Bai and M. Rozlonik, SINUM, 2015
(Chebyshev) Chebyshev acceleration of iterative refinement, M. Arioli and J. Scott, Numerical Algorithms, 66 (2014), 591--608.
(Chebyshev) Chebyshev semi-iteration in preconditioning for problems including the mass matrix, A. Wathen and T. Rees, ETNA, 34 (2009), 125--135.

Miscellaneous

Research and Education in Computational Science and Engineering, SIAM Activity Group on Computational Science and Engineering, SIAM Review, 60 (2018), 707--754.
Report To The President -- Computational Science: Ensuring America’s Competitiveness, President’s Information Technology Advisory Committee, USA, 2005
What is Computational Sciences?
Numerical Analysis, Lloyd N. Trefethen, Princeton Companion to Mathematics, 2008
History of Numerical Linear Algebra, a Personal View, Gene H. Golub, 2007
Is Numerical Analysis Boring, Francis Sullivan, 2006
Predictions for scientific computing 50 years from now, Lloyd N. Trefethen, Mathematics Today, 2000
The Definition of Numerical Analysis, Lloyd N. Trefethen, 1992

Guest Editors Introduction to the top 10 algorithms, J. Dongarra and F. Sullivan, COMPUT SCI ENG, 2(2000), 22-23
The Best of the 20th Century: Editors Name Top 10 Algorithms, Barry A. Cipra, SIAM News, 2000
The Top 10 Computational Methods of the 20th Century, D. Givoli, IACM Expressions, 11 (2001), 5-9.
From Numerical Analysis to Computational Science, B. Engquist and G. Golub, 2001.

How To Give a Talk (ppt), T. Kolda, Sandia National Labs, 2007
What is good mathematics, Terence Tao, 2007
OBITUARY: Gene H. Golub, Lloyd N. Trefethen, Nature, 2007

Trefethen's list of 13 classic papers in applied mathematics

(NA-net posting of 9 May 1993)

J.W. Cooley & J.W. Tukey (1965) -- the Fast Fourier Transform
An algorithm for the machine calculation of complex Fourier series, Math. Comp., 19 (1965), 297--301.
R. Courant, K. Friedrichs & H. Lewy (1928) -- finite difference methods for PDE
On the partial difference equations of mathematical physics, IBM J. Res. Develop., 11 (1967), 215--234.
(originally appeared in Mathematische Annalen, 100 (1928) 32--74)
A.S. Householder (1958) -- QR factorization of matrices
Unitary triangularization of a nonsymmetric matrix, J. Assoc. Comput. Mach., 5 (1958), 339--342.
C.F. Curtiss and J.O. Hirschfelder (1952) -- stiffness of ODEs; BD formulas
Integration of stiff equations, Proc. Nat. Acad. Sci. U.S.A., 38 (1952), 235--243.
C. de Boor (1972) -- calculations with B-splines
On calculating with B-splines, J. Approximation Theory, 6 (1972), 50--62.
R. Courant (1943) -- finite element methods for PDE
Variational methods for the solution of problems of equilibrium and vibrations, Bull. Amer. Math. Soc., 49 (1943), 1--23.
G. Golub and W. Kahan (1965) -- the singular value decomposition
Calculating the singular values and pseudo-inverse of a matrix, J. SIAM Numer. Anal. Ser. B, 2 (1965), 205--224.
A. Brandt (1977) -- multigrid algorithms
Multi-level adaptive solutions to boundary-value problems, Math. Comp., 31/138 (1977), 333--390.
M.R. Hestenes and E. Stiefel (1952) -- the conjugate gradient iteration
Methods of conjugate gradients for solving linear systems, J. Research Nat. Bur. Standards, 49 (1952), 409--436.
R. Fletcher and M.J.D. Powell (1963) -- optimization via quasi-Newton updates
A rapidly convergent descent method for minimization, Comput. J., 6 (1963/1964), 163--168.
G. Wanner, E. Hairer, and S.P. Norsett (1978) -- order stars and applications to ODE
Order stars and stability theorems, BIT, 18 (1978), 475--489.
N. Karmarkar (1984) -- interior point methods for linear programming
A new polynomial-time algorithm for linear programming, Combinatorica, 4 (1984), 373--395.
L. Greengard and V. Rokhlin (1987) -- multipole methods for particles
A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), 325--348.

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