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On rates of acceleration of extrapolation methods for oscillatory infinite integrals

  • Part II Numerical Mathematics
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Abstract

The purpose of this work is to complement and expand our knowledge of the convergence theory of some extrapolation methods for the accurate computation of oscillatory infinite integrals. Specifically, we analyze in detail the convergence properties of theW- and\(\bar D\)-transformations of the author as they are applied to three integrals, all with totally different behavior at infinity. The results of the analysis suggest different convergence and acceleration of convergence behavior for the above mentioned transformations on the different integrals, and they improve considerably those that can be obtained from the existing convergence theories.

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References

  1. W. F. Ford and A. Sidi,An algorithm for a generalization of the Richardson extrapolation process, SIAM J. Numer. Anal., 24 (1987), pp. 1212–1232.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Levin,Development of non-linear transformations for improving convergence of sequences, Internat. J. Comput. Math., B3 (1973), pp. 371–388.

    Article  Google Scholar 

  3. D. Levin, and A. Sidi,Two new classes of non-linear transformations for accelerating the convergence of infinite integrals and series, Appl. Math. Comp., 9 (1981), pp. 175–215.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Sidi,Some properties of a generalization of the Richardson extrapolation process, J. Inst. Math. Applics., 24 (1979), pp. 327–346.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Sidi,Analysis of convergence of the T-transformation for power series, Math. Comp., 35 (1980), pp. 851–874.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Sidi,Extrapolation methods for oscillatory infinite integrals, J. Inst. Math. Applics., 26 (1980), pp. 1–20.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Sidi,The numerical evaluation of very oscillatory infinite integrals by extrapolation, Math. Comp., 38 (1982), pp. 517–529.

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Sidi,An algorithm for a special case of a generalization of the Richardson extrapolation process, Numer. Math., 38 (1982), pp. 299–307.

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Sidi,Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability, J. Comp. Appl. Math., 17 (1987), pp. 105–114.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Sidi,Generalizations of Richardson extrapolation with applications to numerical integration, inNumerical Integration III, (1988) (eds. H. Brass and G. Hämmerlin), pp. 237–250.

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  1. Computer Science Department, Technion — Israel Institute of Technology, 32000, Haifa, Israel

    Avram Sidi

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  1. Avram Sidi
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Sidi, A. On rates of acceleration of extrapolation methods for oscillatory infinite integrals. BIT 30, 347–357 (1990). https://doi.org/10.1007/BF02017353

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  • DOI: https://doi.org/10.1007/BF02017353

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