- 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.

- Introduction ot Numerical Analysis by R. Bulirsch and J. Stoer, 1992.
- Analysis of Numerical Methods by E. Isaacson and H.B. Keller, 1994. (This is a Dover book and is very inexpensive)

- 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, 1991.
- Methods of Numerical Integration , by P. Davis and P. Rabinowitz, 1975.

- "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 (1965), 297-301.
- "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), 215-234.
- "Unitary triangularization of a nonsymmetric matrix," by A. S. Householder, 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.

ccollins@math.utk.edu