Error analysis of Miller’s recurrence algorithm
Author:
F. W. J. Olver
Journal:
Math. Comp. 18 (1964), 6574
MSC:
Primary 65.80
DOI:
https://doi.org/10.1090/S00255718196401694069
MathSciNet review:
0169406
Fulltext PDF Free Access
Abstract  References  Similar Articles  Additional Information
Abstract: Miller’s algorithm is a device for computing the most rapidly decreasing solution of a secondorder linear difference equation. In this paper strict upper bounds are given for the errors in the values yielded by the algorithm, and general conclusions are drawn concerning the accuracy of the process.

British Association For The Advancement Op Science, “Bessel functions, Part II,” Mathematical Tables, v. X, Cambridge University Press, 1952.
 C. W. Jones, A short table for the Bessel functions $I_{n+1/2}(x),\frac 2{\pi }K_{n+1/2}(x)$, Cambridge, at the University Press, 1952. Prepared on behalf of the Mathematical Tables Committee of the Royal Society. MR 0051573
 L. Fox, A short table for Bessel functions of integer orders and large arguments, Royal Society Shorter Mathematical Tables, No. 3, Cambridge, at the University Press, 1954. MR 0065245 F. J. Corbató, “On the computation of auxiliary functions for twocenter integrals by means of a highspeed computer,” J. Chem. Phys., v. 24, 1956, p. 452453.
 Irene A. Stegun and Milton Abramowitz, Generation of Bessel functions on high speed computers, Math. Tables Aids Comput. 11 (1957), 255–257. MR 93939, DOI https://doi.org/10.1090/S00255718195700939393 J. B. Randels & R. F. Reeves, “Note on empirical bounds for generating Bessel functions,” Comm. Assoc. Comput. Mach., v. 1, May 1958, p. 35.
 M. Goldstein and R. M. Thaler, Recurrence techniques for the calculation of Bessel functions, Math. Tables Aids Comput. 13 (1959), 102–108. MR 105794, DOI https://doi.org/10.1090/S00255718195901057945
 Fernando J. Corbató and Jack L. Uretsky, Generation of spherical Bessel functions in digital computers, J. Assoc. Comput. Mach. 6 (1959), 366–375. MR 105792, DOI https://doi.org/10.1145/320986.320991 National Bureau Of Standards, “Handbook of mathematical functions,” Appl. Math. Ser. 55, Government Printing Office, Washington, D. C. (In press.) (Especially Section 9.12, Examples 1 and 7.) M. Abramowitz, Review of a paper by J. Kaye, MTAC, v. 10, 1956, p. 176177.
 Walter Gautschi, Recursive computation of the repeated integrals of the error function, Math. Comp. 15 (1961), 227–232. MR 136074, DOI https://doi.org/10.1090/S00255718196101360749
 A. Rotenberg, The calculation of toroidal harmonics, Math. Comput. 14 (1960), 274–276. MR 0115264, DOI https://doi.org/10.1090/S00255718196001152644
 C. W. Clenshaw, The numerical solution of linear differential equations in Chebyshev series, Proc. Cambridge Philos. Soc. 53 (1957), 134–149. MR 82196, DOI https://doi.org/10.1017/s0305004100032072
 L. Fox, Chebyshev methods for ordinary differential equations, Comput. J. 4 (1961/62), 318–331. MR 136521, DOI https://doi.org/10.1093/comjnl/4.4.318
Retrieve articles in Mathematics of Computation with MSC: 65.80
Retrieve articles in all journals with MSC: 65.80
Additional Information
Article copyright:
© Copyright 1964
American Mathematical Society