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Levin transformations


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1: 3.9 Acceleration of Convergence
§3.9(v) Levin’s and Weniger’s Transformations
We give a special form of Levin’s transformation in which the sequence s = { s n } of partial sums s n = j = 0 n a j is transformed into: …Sequences that are accelerated by Levin’s transformation include logarithmically convergent sequences, i. …
2: 2.11 Remainder Terms; Stokes Phenomenon
Table 2.11.1: Whittaker functions with Levin’s transformation.
n a n s n d n
shows that this direct estimate is correct to almost 3D. The fourth column of Table 2.11.1 gives the results of applying the following variant of Levin’s transformation: …
3: 3.5 Quadrature
Convergence acceleration schemes, for example Levin’s transformation3.9(v)), can be used when evaluating the series. …
4: Bibliography L
  • D. Lemoine (1997) Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions. Comput. Phys. Comm. 99 (2-3), pp. 297–306.
  • E. Levin and D. S. Lubinsky (2001) Orthogonal Polynomials for Exponential Weights. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 4, Springer-Verlag, New York.
  • D. A. Levine (1969) Algorithm 344: Student’s t-distribution [S14]. Comm. ACM 12 (1), pp. 37–38.
  • H. Levine and J. Schwinger (1948) On the theory of diffraction by an aperture in an infinite plane screen. I. Phys. Rev. 74 (8), pp. 958–974.
  • J. Lund (1985) Bessel transforms and rational extrapolation. Numer. Math. 47 (1), pp. 1–14.