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Journal: Math. Comp. 56 (1991), 377-406
DOI: https://doi.org/10.1090/S0025-5718-91-99753-X
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  • [1] D. F. Mayers, Review 24, Math. Comp. 47 (1986), 376-377.
  • [1] Jim Douglas Jr., Todd Dupont, and Lars Wahlbin, Optimal 𝐿_{∞} error estimates for Galerkin approximations to solutions of two-point boundary value problems, Math. Comp. 29 (1975), 475–483. MR 0371077, https://doi.org/10.1090/S0025-5718-1975-0371077-0
  • [2] Robert D. Richtmyer and K. W. Morton, Difference methods for initial-value problems, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0220455
  • [3] Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1973. Prentice-Hall Series in Automatic Computation. MR 0443377
  • [4] Mary Fanett Wheeler, An optimal 𝐿_{∞} error estimate for Galerkin approximations to solutions of two-point boundary value problems, SIAM J. Numer. Anal. 10 (1973), 914–917. MR 0343659, https://doi.org/10.1137/0710077
  • [1] W. Albers, Asymptotic expansions and the deficiency concept in statistics, Mathematisch Centrum, Amsterdam, 1974. Mathematical Centre Tracts, No. 58. MR 0381127
  • [2] Tom M. Apostol, Modular functions and Dirichlet series in number theory, Springer-Verlag, New York-Heidelberg, 1976. Graduate Texts in Mathematics, No. 41. MR 0422157
  • [3] William C. Bauldry, Attila Máté, and Paul Nevai, Asymptotics for solutions of systems of smooth recurrence equations, Pacific J. Math. 133 (1988), no. 2, 209–227. MR 941919
  • [4] Imme van den Berg, Nonstandard asymptotic analysis, Lecture Notes in Mathematics, vol. 1249, Springer-Verlag, Berlin, 1987. MR 887738
  • [5] George D. Birkhoff, Formal theory of irregular linear difference equations, Acta Math. 54 (1930), no. 1, 205–246. MR 1555307, https://doi.org/10.1007/BF02547522
  • [6] George D. Birkhoff and W. J. Trjitzinsky, Analytic theory of singular difference equations, Acta Math. 60 (1933), no. 1, 1–89. MR 1555364, https://doi.org/10.1007/BF02398269
  • [7] N. Bleistein and R. A. Handelsman, Asymptotic expansions of integrals, Holt, Rinehart and Winston, New York, 1975.
  • [8] Clifford O. Bloom and Nicholas D. Kazarinoff, Short wave radiation problems in inhomogeneous media: asymptotic solutions, Lecture Notes in Mathematics, Vol. 522, Springer-Verlag, Berlin-New York, 1976. MR 0470439
  • [9] Albrecht Böttcher and Bernd Silbermann, Invertibility and asymptotics of Toeplitz matrices, Mathematical Research, vol. 17, Akademie-Verlag, Berlin, 1983. MR 734173
  • [10] A. A. Borovkov, Asymptotic methods in queuing theory, Chichester, New York, 1984.
  • [11] N. G. de Bruijn, Asymptotic methods in analysis, North-Holland, Amsterdam, 1961.
  • [12] Edmond Combet, Intégrales exponentielles. Développements asymptotiques, propriétés lagrangiennes, Lecture Notes in Mathematics, vol. 937, Springer-Verlag, Berlin-New York, 1982 (French). Mathematical Centre Tracts, 105. MR 665746
  • [13] E. T. Copson, Asymptotic expansions, Cambridge Tracts in Mathematics, vol. 55, Cambridge University Press, Cambridge, 2004. Reprint of the 1965 original. MR 2139829
  • [14] Miklós Csörgő, Sándor Csörgő, and Lajos Horváth, An asymptotic theory for empirical reliability and concentration processes, Lecture Notes in Statistics, vol. 33, Springer-Verlag, Berlin, 1986. MR 856407
  • [15] R. B. Dingle, Asymptotic expansions: their derivation and interpretation, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], London-New York, 1973. MR 0499926
  • [16] R. J. M. M. Does, Higher order asymptotics for simple linear rank statistics, Mathematical Centre Tracts, vol. 151, Mathematisch Centrum, Amsterdam, 1982. MR 677673
  • [17] Wiktor Eckhaus, Matched asymptotic expansions and singular perturbations, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973. North-Holland Mathematics Studies, No. 6. MR 0670800
  • [18] A. Erdélyi, Asymptotic expansions, Dover Publications, Inc., New York, 1956. MR 0078494
  • [19] S. F. Feshchenko, Asymptotic methods in the theory of linear differential equations, NASA, Washington, D.C., 1967.
  • [20] Walter B. Ford, Studies on divergent series and summability & The asymptotic developments of functions defined by Maclaurin series, Chelsea Publishing Co., New York, 1960. MR 0115035
  • [21] Johan Grasman, Asymptotic methods for relaxation oscillations and applications, Applied Mathematical Sciences, vol. 63, Springer-Verlag, New York, 1987. MR 884527
  • [22] J. Heading, An introduction to phase-integral methods, Methuen & Co., Ltd., London; John Wiley & Sons, Inc., New York, 1962. MR 0148995
  • [23] P. W. Hemker, The numerical solution of a singular perturbation problem in the domain exterior of a circle, Mathematisch Centrum, Amsterdam, 1974. Mathematisch Centrum, Afdeling Numerieke Wiskunde NW 11/74. MR 0383793
  • [24] I. I. Hirschman Jr. and Daniel E. Hughes, Extreme eigenvalues of Toeplitz operators, Lecture Notes in Mathematics, Vol. 618, Springer-Verlag, Berlin-New York, 1977. MR 0493488
  • [25] I. A. Ibragimov and R. Z. Has′minskiĭ, Statistical estimation, Applications of Mathematics, vol. 16, Springer-Verlag, New York-Berlin, 1981. Asymptotic theory; Translated from the Russian by Samuel Kotz. MR 620321
  • [26] Geertrui K. Immink, Asymptotics of analytic difference equations, Lecture Notes in Mathematics, vol. 1085, Springer-Verlag, Berlin, 1984. MR 765699
  • [27] Victor Ivriĭ, Precise spectral asymptotics for elliptic operators acting in fiberings over manifolds with boundary, Lecture Notes in Mathematics, vol. 1100, Springer-Verlag, Berlin, 1984. MR 771297
  • [28] Harold Jeffreys, Asymptotic approximations, Clarendon Press, Oxford, 1962. MR 0147821
  • [29] P. A. Lagerstrom, Matched asymptotic expansions, Applied Mathematical Sciences, vol. 76, Springer-Verlag, New York, 1988. Ideas and techniques. MR 958913
  • [30] H. A. Lauwerier, Asymptotic analysis, Mathematisch Centrum, Amsterdam, 1974. Mathematical Centre Tracts, No. 54. MR 0467123
  • [31] A. H. Lightstone and Abraham Robinson, Nonarchimedean fields and asymptotic expansions, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. North-Holland Mathematical Library, Vol. 13. MR 0414354
  • [32] D. S. Lubinsky, Strong asymptotics for extremal asymptotics associated with weights on $ ( - \infty , + \infty )$, Springer-Verlag, Berlin and New York, 1988.
  • [33] Stephen McAdam, Asymptotic prime divisors, Lecture Notes in Mathematics, vol. 1023, Springer-Verlag, Berlin, 1983. MR 722609
  • [34] J. D. Murray, Asymptotic analysis, 2nd ed., Applied Mathematical Sciences, vol. 48, Springer-Verlag, New York, 1984. MR 740864
  • [35] G. A. Nariboli, Asymptotic theory of wave motion in rods, Engineering Research Institute, Iowa State University, Ames, Iowa, 1968.
  • [36] Ali Hasan Nayfeh, Perturbation methods, John Wiley & Sons, New York-London-Sydney, 1973. Pure and Applied Mathematics. MR 0404788
  • [37] Paul G. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc. 18 (1979), no. 213, v+185. MR 519926, https://doi.org/10.1090/memo/0213
  • [38] Robert E. O’Malley Jr., Introduction to singular perturbations, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Applied Mathematics and Mechanics, Vol. 14. MR 0402217
  • [39] F. W. J. Olver, Asymptotics and special functions, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Computer Science and Applied Mathematics. MR 0435697
  • [40] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York-Heidelberg, 1975. Translated from the Russian by A. A. Brown; Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 82. MR 0388499
  • [41] Franz Pittnauer, Vorlesungen über asymptotische Reihen, Lecture Notes in Mathematics, Vol. 301, Springer-Verlag, Berlin-New York, 1972 (German). MR 0617763
  • [42] È. Ya. Riekstyn′sh, \cyr Asimptoticheskie razlozheniya integralov. Tom 3, “Zinatne”, Riga, 1981 (Russian). MR 640098
  • [43] Charles Rockland, Hypoellipticity and eigenvalue asymptotics, Lecture Notes in Mathematics, Vol. 464, Springer-Verlag, Berlin-New York, 1975. MR 0501202
  • [44] Maurice Roseau, Asymptotic wave theory, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1976. North-Holland Series in Applied Mathematics and Mechanics, Vol. 20. MR 0433015
  • [45] W. P. M. de Ruijter, On the asymptotic analysis of large-scale ocean circulation, Mathematical Centre Tracts, vol. 120, Mathematisch Centrum, Amsterdam, 1980. MR 564657
  • [46] Harry S. Rutten, Theory and design of shells on the basis of asymptotic analysis, Rutten and Kruisman, Rijswijk, Netherlands, 1973.
  • [47] Yasutaka Sibuya, Global theory of a second order linear ordinary differential equation with a polynomial coefficient, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. North-Holland Mathematics Studies, Vol. 18. MR 0486867
  • [48] Carl Ludwig Siegel, Beitrag zum Problem der Stabilität, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 3 (1974), 23–58. MR 0399605
  • [49] L. Sirovich, Techniques of asymptotic analysis, Applied Mathematical Sciences, Vol. 2, Springer-Verlag, New York-Berlin, 1971. MR 0275034
  • [50] V. K. Varadan and V. V. Varadan (eds.), Low and high frequency asymptotics, Mechanics and Mathematical Methods. A Series of Handbooks. Series III: Acoustic, Electromagnetic and Elastic Wave Scattering, vol. 2, North-Holland Publishing Co., Amsterdam, 1986. MR 901960
    R. E. Kleinman and T. B. A. Senior, Rayleigh scattering, Low and high frequency asymptotics, Mech. Math. Methods. Ser. Handbooks. Ser. III Acoust. Electromagnet. Elastic Wave Scatt., vol. 2, North-Holland, Amsterdam, 1986, pp. 1–70. MR 901961, https://doi.org/10.1016/B978-0-444-87726-0.50006-9
  • [51] Walter Van Assche, Asymptotics for orthogonal polynomials, Lecture Notes in Mathematics, vol. 1265, Springer-Verlag, Berlin, 1987. MR 903848
  • [52] Wolfgang Wasow, Asymptotic expansions for ordinary differential equations, Pure and Applied Mathematics, Vol. XIV, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR 0203188
  • [53] Jet Wimp, Uniform scale functions and the asymptotic expansion of integrals, Ordinary and partial differential equations (Proc. Fifth Conf., Univ. Dundee, Dundee, 1978) Lecture Notes in Math., vol. 827, Springer, Berlin, 1980, pp. 251–271. MR 610820
  • [54] R. Kh. Zeytounian, Les modèles asymptotiques de la mécanique des fluides. I, Lecture Notes in Physics, vol. 245, Springer-Verlag, Berlin, 1986 (French). MR 878567
  • [1] Frederick N. Fritsch, Review 3, Math. Comp. 50 (1988), 346-348.
  • [1] Peter Lane, Nick Galwey & Norman Alvey, Genstat 5-An Introduction, Clarendon Press, Oxford, 1987. Review 4, Math. Comp. 52 (1989), 252.
  • [1] V. E. Hoggatt, Jr., Fibonacci and Lucas numbers, Houghton Mifflin, New York, 1969.
  • [2] N. N. Vorob′ev, Fibonacci numbers, Translated from the Russian by Halina Moss; translation editor Ian N. Sneddon, Blaisdell Publishing Co. (a division of Random House), New York-London, 1961. MR 0146138


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DOI: https://doi.org/10.1090/S0025-5718-91-99753-X
Article copyright: © Copyright 1991 American Mathematical Society