Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Note on backward recurrence algorithms


Authors: F. W. J. Olver and D. J. Sookne
Journal: Math. Comp. 26 (1972), 941-947
MSC: Primary 65Q05; Secondary 33A40
MathSciNet review: 0331826
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An algorithm is given for the computation of the recessive solution of a secondorder linear difference equation, based upon a combination of algorithms due to J.C.P. Miller and F.W.J. Olver. A special feature is automatic and rigorous control of truncation error.

The method is illustrated by application to the well-used example of the Bessel functions $ {J_r}(x)$.


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

  • [1] Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24–82. MR 0213062 (35 #3927)
  • [2] British Association for the Advancement of Science, ``Bessel functions. Part II,'' Mathematical Tables, v. 10, Cambridge University Press, Cambridge, 1952.
  • [3] F. W. J. Olver, Numerical solution of second-order linear difference equations, J. Res. Nat. Bur. Standards Sect. B 71B (1967), 111–129. MR 0221789 (36 #4841)
  • [4] John G. Wills, On the use of recursion relations in the numerical evaluation of spherical Bessel functions and Coulomb functions, J. Computational Phys. 8 (1971), 162–166. MR 0298890 (45 #7939)
  • [5] F. W. J. Olver, Bounds for the solutions of second-order linear difference equations, J. Res. Nat. Bur. Standards Sect. B 71B (1967), 161–166. MR 0229407 (37 #4981)
  • [6] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746 (6,64a)
  • [7] W. Kahan, ``Note on bounds for generating Bessel functions by recurrence.'' (Unpublished.)
  • [8] D. Jordan, Argonne National Laboratory Library Routine, ANL C370S--BESJY, October 1967.
  • [9] Saburo Makinouchi, Note on the recurrence techniques for the calculation of Bessel functions 𝐽ᵥ(𝑥), Tech. Rep. Osaka Univ. 16 (1965), 185–201. MR 0198658 (33 #6813)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65Q05, 33A40

Retrieve articles in all journals with MSC: 65Q05, 33A40


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1972-0331826-1
PII: S 0025-5718(1972)0331826-1
Keywords: Bessel functions, difference equations, error bounds, FORTRAN, Miller algorithm, recursion
Article copyright: © Copyright 1972 American Mathematical Society