Books which provide a basic introduction to Numerical Analysis at
or below the level of our book:
Books which provide a basic introduction to Numerical Analysis at a
higher level than our book:
- Numerical Analysis by D. Kincaid and W. Cheney, 1991.
- Introduction to Scientific Computing by Charles F. Van Loan, 1997.
- Numerical Methods for Mathematics, Science, and Engineering by John H. Mathews, 1992.
- Numerical Analysis: A Practical Approach by Melvin Maron and
Robert Lopez, 1991.
- Elementary Numerical Analysis: An Algorithmic Approach by
Conte and de Boor, 1980.
- Numerical Mathematics and Computing by Cheney and Kincaid, 1999.
Books of a more specialized nature:
- Introduction ot Numerical Analysis by R. Bulirsch and J.
- Analysis of Numerical Methods by E. Isaacson and H.B.
Keller, 1994. (This is a Dover book and is very inexpensive)
Some interesting books, papers, etc:
- Matrix Computations, 3rd Edition , by G. Golub and C. Van Loan.
- Introduction to Numerical Linear Algebra and Optimisation , by P. Ciarlet, 1989.
- Numerical Methods for Unconstrained Optimization , by J.E. Dennis and
R. Schnabel, 1983.
- Numerical Methods for Ordinary Differential Systems , by J.D. Lambert,
- Methods of Numerical Integration , by P. Davis and P. Rabinowitz, 1975.
Original sources for some classic algorithms:
- "What every computer scientist should know about
floating-point arithmetic," by David Goldberg, ACM Computing Surveys, 23 (March 1992) 5-48. (Postscript Copy)
- "An algorithm for the machine
calculation of complex Fourier series," by James W. Cooley and
John W. Tukey, Mathematics of Computation 19
- "Ueber die partiellen
Differenzengleichungen der mathematischen Physik," by R. Courant,
K. O. Friedrichs and H. Lewy, Mathematische Annalen
100 (1928), 32-74. Translated as: "On the partial difference equations of
mathematical physics," IBM Journal of Resarch and Development 11 (1967),
- "Unitary triangularization of a nonsymmetric matrix," by A. S.
Journal of the Association of Computing Machinery 5 (1958), 339-342.
- "Integration of stiff equations," by C. F. Curtiss and J. O. Hirschfelder,
Proceedings of the National Academy of Sciences 38 (1952), 235-243.
- "On calculating with B-splines," by C. de Boor, Journal of Approximation
Theory 6 (1972), 50-62.
- "Variational methods for the solution of problems of
equilibrium and vibrations," by R. Courant, Bulletin of the American Mathematical Society
49 (1943), 1-23.
- "Calculating the singular values and pseudo-inverse
of a matrix," by G. Golub and W. Kahan, SIAM Journal on Numerical Analysis 2 (1965), 205-224.
- "Multi-level adaptive solutions to boundary-value problems,"
by A. Brandt,
Mathematics of Computation 31 (1977), 333-390.
- "Methods of conjugate gradients for
solving linear systems," by Magnus R. Hestenes and Eduard Stiefel, Journal of Research of the National Bureau of
Standards 49 (1952), 409-436.
- "A rapidly convergent descent method for
minimization," by R. Fletcher and M. J. D. Powell, Computer Journal 6 (1963), 163-168.
- "Order stars and stability
theorems," by G. Wanner, E. Hairer and S. P. Norsett, BIT 18 (1974), 475-489.
- "A new polynomial-time algorithm for linear programming," by N. Karmarkar,
Combinatorica 4 (1984), 373-395.
- "A fast algorithm for particle simulations," by L. Greengard and V. Rokhlin,
Journal of Computational Physics 72 (1987), 325-348.
Last Modified: July 26, 2000