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An extension of Olver's error estimation technique for linear recurrence relations

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Abstract

When unstable rounding error propagation prevents a linear recurrence relation being solved recursively a sufficiently accurate solution may be determined in certain cases by an inexact but well-conditioned boundary-value problem. An algorithm, based on that ofOlver for second order relations, is given for estimating the truncation error in the general case, and a practical computational technique developed for relations having solutions of exponential type.

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References

  1. 1.

    British Association for the Advancement of Science: Bessel functions, part II. Mathematical tables, Vol. X. Cambridge: Cambridge University Press 1952.

  2. 2.

    Oliver, J.: Relative error propagation in the recursive solution of linear recurrence relations. Numer. Math.9, 323–340 (1967).

  3. 3.

    ——: The numerical solution of linear recurrence relations. Numer. Math.11, 349–360 (1968).

  4. 4.

    Olver, F. W. J.: Error analysis ofMiller's recurrence algorithm. Math. Comp.18, 65–74 (1964).

  5. 5.

    ——: Numerical solution of second-order linear difference equations. J. Res. N.B.S.71B, 111–129 (1967).

  6. 6.

    ——: Bounds for the solutions of second-order linear difference equations. J. Res. N.B.S.71B, 161–166 (1967).

  7. 7.

    Tait, R.: Error analysis of recurrence equations. Math. Comp.21, 629–638 (1967).

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Oliver, J. An extension of Olver's error estimation technique for linear recurrence relations. Numer. Math. 12, 459–467 (1968). https://doi.org/10.1007/BF02161370

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Keywords

  • Error Estimation
  • Mathematical Method
  • Recurrence Relation
  • Estimation Technique
  • Error Propagation