- [AH01]
- Kendall Atkinson and Weimin Han,
*Theoretical Numerical Analysis, a Functional Analysis Framework*, Springer, 2001. - [B78]
- Carl de Boor,
*A Practical Guide to Splines,*Springer, 1978. - [BN01]
- Albert Boggess and Francis J. Narcowich,
*A First Course in Wavelets with Fourier Analysis,*Prentice-Hall, 2001. - [BT04]
- Jean-Paul Berrut and Lloyd N. Trefethen,
*Barycentric Lagrangian interpolation,*SIAM Review 46 (2004), pp. 501-517. - [CGGR00]
- D. Calvetti, G. H. Golub, W. B. Gragg, and L. Reichel,
*Computation of Gauss-Kronrod Quadrature Rules.*Math. Comput. 69, 2000, pp. 1035-1052. - [Ch66]
- E. W. Cheney,
*Introduction to Approximation Theory,*McGraw-Hill, 1966. A second edition is available from Chelsea Publishing Company at reasonable cost. This is just the first edition with corrections. - [C78]
- P. G. Ciarlet,
*The Finite Element Method for Elliptic Problems,*North Holland, 1978. - [H04]
- Nicholas J. Higham,
*The numerical stability of barycentric Lagrangian interpolation,*IMA J. Numer. Anal. 54 (2004), pp. 547-556. - [KC02]
- David R. Kincaid and E. Ward Cheney,
*Numerical Analysis, Mathematics of Scientific Computing,*Third Edition, Brooks/Cole, 2002. - [K88]
- T. W. Korner (Koerner),
*Fourier Analysis,*Cambridge University Press, 1988. - [Ph03]
- George M. Phillips,
*Interpolation and Approximation by Polynomials,*Springer, 2003. - [R69]
- Theodore J. Rivlin,
*An Introduction to the Approximation of Functions,*Dover, 1969. - [S89]
- Gilbert Strang,
*Wavelets and dilation equations: a brief introduction,*SIAM Review 31, 1989, pp. 614-627. - [SN96]
- Gilbert Strang and Truong Nguyen,
*Wavelets and Filter Banks,*Wellesley-Cambridge Press, 1996. - [T00]
- L. N. Trefethen,
*Spectral Methods in MATLAB,*SIAM, 2000. - [W93]
- David S. Watkins,
*Some perspectives on the eigenvalue problem,*SIAM Review 35 (1993), pp. 430-471.

- Best least-first-power (L_{1}) approximation [R69]
- Rational approximation, Pade approximation [Ch66] (Hung)
- Jackson's Theorem [R69] (Sherod)
- Characterization of best uniform approximation, equi-oscillation theorem [Ch66,Ph03,R69]
- Computing the the best uniform approximation, Remez exchange algorithm [Ch6,Ph03,R69]
- Basics of spectral methods [T00]
- Basics of finite element methods [AH01], [C78]
- Computing Gaussian quadrature points and weights from eigenvalues/vectors of a tridiagonal matrix [W93] (Andrei)
- Gauss-Kronrod quadrature [CGGR00]
- Effectiveness of least-squares approximants as uniform approximants [R69]
- Peano kernel theorem and applications [Ph03]
- Divided differences and Hermite interpolation [KC02]
- something on splines
- The fast Fourier transform (Xunning)
- Heisenberg uncertainty principal [BN01] (and many other sources) (Lisa)
- Something on data compression, e.g. JPEG 2000