About the Project
NIST

numerical inversion

AdvancedHelp

(0.002 seconds)

1—10 of 35 matching pages

1: 8.25 Methods of Computation
A numerical inversion procedure is also given for calculating the value of x (with 10S accuracy), when a and P ( a , x ) are specified, based on Newton’s rule (§3.8(ii)). …
2: Bibliography E
  • U. T. Ehrenmark (1995) The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature. J. Comput. Appl. Math. 61 (1), pp. 43–72.
  • 3: 3.11 Approximation Techniques
    Laplace Transform Inversion
    Numerical inversion of the Laplace transform (§1.14(iii)) …
    4: 3.5 Quadrature
    Example. Laplace Transform Inversion
    A special case is the rule for Hilbert transforms (§1.14(v)): …
    5: 4.45 Methods of Computation
    4.45.8 2 arctan x 1 + ( 1 + x 2 ) 1 / 2 = arctan x , 0 < x < .
    4.45.9 x n = x n - 1 1 + ( 1 + x n - 1 2 ) 1 / 2 , n = 1 , 2 , 3 , ,
    6: Bibliography S
  • H. E. Salzer (1955) Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms. Math. Tables Aids Comput. 9 (52), pp. 164–177.
  • 7: Brian D. Sleeman
    Sleeman has published numerous papers in applied analysis, multiparameter spectral theory, direct and inverse scattering theory, and mathematical medicine. …
    8: 4.46 Tables
    §4.46 Tables
    Extensive numerical tables of all the elementary functions for real values of their arguments appear in Abramowitz and Stegun (1964, Chapter 4). …
    9: Errata
  • Equations (4.45.8), (4.45.9)

    These equations have been rewritten to improve the numerical computation of arctan x .

  • 10: 22.19 Physical Applications
    Numerous other physical or engineering applications involving Jacobian elliptic functions, and their inverses, to problems of classical dynamics, electrostatics, and hydrodynamics appear in Bowman (1953, Chapters VII and VIII) and Lawden (1989, Chapter 5). …