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Deuflhard, P.

A summation technique for minimal solutions of linear homogeneous difference equations. (English) Zbl 0348.65091

Computing 18, 1-13 (1977).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0348.65091

Cited in 1 Review
Cited in 5 Documents

MSC:

65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
39A10 Additive difference equations
65F10 Iterative numerical methods for linear systems
65D10 Numerical smoothing, curve fitting
65G50 Roundoff error
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References:

[1] Abromowitz, M., Stegun, I. A. (eds.): Handbook of Mathematical Functions. New York: Dover Publ. 1965.
[2] Barth, W., Martin, R. S., Wilkinson, J. H.: Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection. Numer. Math.9, 386–393 (1967). · Zbl 0189.47803 · doi:10.1007/BF02162154
[3] Brand, L.: Differential and Difference Equations. New York: Wiley 1966. · Zbl 0223.34001
[4] Bulirsch, R., Stoer, J.: Darstellung von Funktionen in Rechenautomaten in [16]. S. 352–445.
[5] Clenshaw, C. W.: A note on the summation of Chebyshev series. MTAC9, 118–120 (1955). · Zbl 0065.05403
[6] Deuflhard, P.: On Algorithms for the Summation of Certain Special Functions. Computing17, 37–48 (1976). · Zbl 0331.65011 · doi:10.1007/BF02252258
[7] Gautschi, W.: Computational aspects of three-term recurrence relations. SIAM Rev.9, 24–82 (1967). · Zbl 0168.15004 · doi:10.1137/1009002
[8] Goertzel, G.: An Algorithm for the Evaluation of Finite Trigonometric Series. Amer. Math. Monthly65, 34–35 (1958). · Zbl 0079.13910 · doi:10.2307/2310304
[9] Meixner, J., Schäfke, W.: Mathieusche Funktionen und Sphäroidfunktionen. Berlin-Göttingen-Heidelberg: Springer 1954. · Zbl 0058.29503
[10] Miller, J. C. P.: Bessel functions, Part II (Math. Tables X). Cambridge University Press 1952.
[11] Olver, F. W. J.: Error Analysis of Miller’s Recurrence Algorithm. Math. Comp.18, 65–74 (1964). · Zbl 0115.34502
[12] Olver, F. W. J.: Numerical Solution of Second-Order Linear Difference Equations. J. Res. N.B.S.71B, 111–129 (1967). · Zbl 0171.36601
[13] Olver, F. W. J., Sookne, D. J.: Note on Backward Recurrence Algorithms. Math. Comp.26, 941–947 (1972). · Zbl 0261.65080 · doi:10.1090/S0025-5718-1972-0331826-1
[14] Perron, O.: Die Lehre von den Kettenbrüchen. Stuttgart: Teubner (Bd. I.: 1954, Bd. II: 1957). · Zbl 0077.06602
[15] Reinsch, Chr.: A Note on Trigonometric Interpolation. Unpublished Manuscript (results available in [4].
[16] Sauer, R., Szabò, I. (eds.): Mathematische Hilfsmittel des Ingenieurs, Teil III. Berlin-Heidelberg-New York: Springer 1968. · Zbl 0193.35201
[17] Shintani, H.: Note on Miller’s Recurrence Algorithm. J. Sci. Hiroshima Univ. Ser.A-I29, 121–133 (1965). · Zbl 0135.38703
[18] Stoer, J.: Einführung in die Numerische Mathematik I. Berlin-Heidelberg-New York: Springer 1972. (HTB 105.) · Zbl 0245.65001
[19] Wilkinson, J. H.: The Algebraic Eigenvalue Problem. Oxford: Clarendon Press 1965. · Zbl 0258.65037
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