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1: 3.8 Nonlinear Equations
Bisection Method
Secant Method
Eigenvalue Methods
2: 19.36 Methods of Computation
§19.36 Methods of Computation
§19.36(i) Duplication Method
When the differences are moderately small, the iteration is stopped, the elementary symmetric functions of certain differences are calculated, and a polynomial consisting of a fixed number of terms of the sum in (19.19.7) is evaluated. … For computation of Legendre’s integral of the third kind, see Abramowitz and Stegun (1964, §§17.7 and 17.8, Examples 15, 17, 19, and 20). …
§19.36(iv) Other Methods
3: Bibliography S
  • B. I. Schneider, X. Guan, and K. Bartschat (2016) Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation. Adv. Quantum Chem. 72, pp. 95–127.
  • M. J. Seaton (1984) The accuracy of iterated JWBK approximations for Coulomb radial functions. Comput. Phys. Comm. 32 (2), pp. 115–119.
  • J. Segura (1998) A global Newton method for the zeros of cylinder functions. Numer. Algorithms 18 (3-4), pp. 259–276.
  • J. Segura (2001) Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros. Math. Comp. 70 (235), pp. 1205–1220.
  • F. Stenger (1993) Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.