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Note on backward recurrence algorithms. (English) Zbl 0261.65080


MSC:

65Q05 Numerical methods for functional equations (MSC2000)
65D20 Computation of special functions and constants, construction of tables
15A06 Linear equations (linear algebraic aspects)
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
39A10 Additive difference equations
40A25 Approximation to limiting values (summation of series, etc.)
65G50 Roundoff error
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References:

[1] Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24 – 82. · Zbl 0168.15004 · doi:10.1137/1009002
[2] British Association for the Advancement of Science, “Bessel functions. Part II,” Mathematical Tables, v. 10, Cambridge University Press, Cambridge, 1952. · JFM 63.1144.03
[3] F. W. J. Olver, Numerical solution of second-order linear difference equations, J. Res. Nat. Bur. Standards Sect. B 71B (1967), 111 – 129. · Zbl 0171.36601
[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. · Zbl 0219.65019
[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. · Zbl 0178.09702
[6] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. · Zbl 0063.08184
[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 (Unpublished.)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 \?\?(\?), Tech. Rep. Osaka Univ. 16 (1965), 185 – 201.
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