Chapter 3 Numerical Methods

Acknowledgements:

The author thanks W. Gautschi and C. Brezinski for their valuable contributions, and F. W. J. Olver for assisting with the writing of §§3.6, 3.7, 3.8, and 3.11.

Notes:

Lozier and Olver (1994) gives an overview of the numerical evaluation of special functions. For more detailed information see Gautschi (1997a), Gil et al. (2007a), Henrici (1974, 1977, 1986), Hildebrand (1974), Luke (1969a, b), and Trefethen (2011).

Referenced by:

Profile Amparo Gil, Profile Javier Segura, Profile Nico M. Temme, Profile Nico M. Temme, § Chapter Authors, § Associate Editors, § Associate Editors, § Associate Editors, Other Changes, Methodology

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Addition (effective with 1.0.5):

Trefethen (2011) was added as a general reference for this chapter.

Reported 2012-10-01

• Areas
  • 3.1 Arithmetics and Error Measures
  • 3.2 Linear Algebra
  • 3.3 Interpolation
  • 3.4 Differentiation
  • 3.5 Quadrature
  • 3.6 Linear Difference Equations
  • 3.7 Ordinary Differential Equations
  • 3.8 Nonlinear Equations
  • 3.9 Acceleration of Convergence
  • 3.10 Continued Fractions
  • 3.11 Approximation Techniques
  • 3.12 Mathematical Constants