Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

The $ T\sb{+m}$ translformation


Author: Roland F. Streit
Journal: Math. Comp. 30 (1976), 505-511
MSC: Primary 65B10
MathSciNet review: 0421028
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper discusses a nonlinear sequence-to-sequence transformation, known as the $ {T_{ + m}}$ transform, which is used to accelerate the convergence of an infinite series. A brief history of the transform is given; a number of theorems are established which enable one to make effective use of the transform, and several examples are presented to illustrate this effectiveness.


References [Enhancements On Off] (What's this?)

  • [1] A. C. AITKEN, "On Bernoulli's numerical solution of algebraic equations," Proc. Roy. Soc. Edinburgh, v. 46, 1926, pp. 289-305.
  • [2] D. SHANKS & T. S. WALTON, The Use of Rational Functions as Approximate Solutions of Certain Trajectory Problems, Naval Ordnance Laboratory Memorandum #9524, White Oak, Md., 1948.
  • [3] D. R. Hartree, Notes on iterative processes, Proc. Cambridge Philos. Soc. 45 (1949), 230–236. MR 0029268
  • [4] Gabriel Isakson, A method for accelerating the convergence of an iteration procedure, J. Aeronaut. Sci. 16 (1949), 443. MR 0030814
  • [5] FOREST R. MOULTON, Introduction to Celestial Mechanics, MacMillan, New York, 1916, p. 364.
  • [6] Paul A. Samuelson, A convergent iterative process, J. Math. Phys. Mass. Inst. Tech. 24 (1945), 131–134. MR 0014827
  • [7] D. SHANKS, An Analogy Between Transients and Mathematical Sequences and Some Non-Linear Sequence-to-Sequence Transforms Suggested by It. I, Naval Ordnance Laboratory Memorandum #9994, White Oak, Md., 1949.
  • [8] Daniel Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. and Phys. 34 (1955), 1–42. MR 0068901
  • [9] Samuel Lubkin, A method of summing infinite series, J. Research Nat. Bur. Standards 48 (1952), 228–254. MR 0051576
  • [10] H. L. Gray and W. D. Clark, On a class of nonlinear transformations and their applications to the evaluation of infinite series, J. Res. Nat. Bur. Standards Sect. B 73B (1969), 251–274. MR 0267304
  • [11] T. J. I'A. BROMWICH, An Introduction to the Theory of Infinite Series, MacMillan, London, 1908.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65B10

Retrieve articles in all journals with MSC: 65B10


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1976-0421028-6
Article copyright: © Copyright 1976 American Mathematical Society