본문 바로가기
KERD
논문KCI 등재

ERROR ANALYSIS ASSOCIATED WITH UNIFORM HERMITE INTERPOLATIONS OF BANDLIMITED FUNCTIONS

Mahmoud H. Annaby|Rashad M. Asharabi
대한수학회 (The Korean Mathematical Society)|2010.11|대한수학회지 (Journal of the KMS)|제47권 제6호|pp. 1299-1316

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

truncationHermite interpolationsderivative sampling theoremamplitude and jitter errors
주제분류수학

초록

We derive estimates for the truncation, amplitude and jitter type errors associated with Hermite-type interpolations at equidistant nodes of functions in Paley-Wiener spaces. We give pointwise and uniform estimates. Some examples and comparisons which indicate that applying Hermite interpolations would improve the methods that use the classical sampling theorem are given.

Abstract

We derive estimates for the truncation, amplitude and jitter type errors associated with Hermite-type interpolations at equidistant nodes of functions in Paley-Wiener spaces. We give pointwise and uniform estimates. Some examples and comparisons which indicate that applying Hermite interpolations would improve the methods that use the classical sampling theorem are given.

참고문헌 (32)

  1. M. Abramowitz, "Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables" (1972), Dover
  2. H. Alzer, "On some inequalities for the gamma and psi functions", Math. Comp., 66(217), pp.373~389 (1997)
  3. M. H. Annaby, "Truncation, amplitude and jitter errors on R for sampling series derivatives, Submitted", ~
  4. M. H. Annaby, "Approximating eigenvalues of discontinuous problems by sampling theorems", J. Numer. Math., 16(3), pp.163~183 (2008)
  5. M. H. Annaby, "On sinc-based method in computing eigenvalues of boundary-value problems", SIAM J. Numer. Anal., 46(2), pp.671~690 (2008)
  6. M. H. Annaby, "On computing eigenvalues of second-order linear pencils", IMA J. Numer. Anal., 27(2), pp.366~380 (2007)
  7. R. P. Boas, "Entire Functions" (1954), Academic Press
  8. A. Boumenir, "Eigenvalues of S-L systems using sampling theory", Appl. Anal., 62(3), pp.323~334 (1996)
  9. J. L. Brown, Jr., "Bounds for truncation error in sampling expansions of band-limited signals", IEEE Trans. Information Theory, IT-15, pp.440~444 (1969)
  10. P. L. Butzer, "A survey of the Whittaker-Shannon sampling theorem and some of its extensions", J. Math. Res. Exposition, 3(1), pp.185~212 (1983)
  11. P. L. Butzer, "Magnitude of the truncation error in sampling expansions of band-limited signals", IEEE Trans. Acoust. Speech Signal Process, ASSP-30, pp.906~912 (1982)
  12. P. L. Butzer, "Sampling theory of signal analysis, Development of mathematics 1950–2000", pp.193~234 (2000), Birkhauser
  13. P. L. Butzer, "An introduction to sampling analysis, Nonuniform sampling", pp.2001, Kluwer
  14. P. L. Butzer, "On quantization, truncation and jitter errors in the sampling theorem and its generalizations", Signal Process, 2(2), pp.101~112 (1980)
  15. P. L. Butzer, "The sampling theorem and linear prediction in signal analysis", Jahresber. Deutsch. Math.-Verein., 90(1), pp.1~70 (1988)
  16. K. Chandrasekharan, "Classical Fourier Transforms" (1989), Springer-Verlag
  17. G. R. Grozev, "Reconstruction of entire functions from irregularly spaced sample points", Canad. J. Math., 48(4), pp.777~793 (1996)
  18. J. R. Higgins, "Sampling Theory in Fourier and Signal Analysis Foundations" (1996), Oxford University Press
  19. J. R. Higgins, "The sampling theorem and several equivalent results in analysis", J. Comput. Anal. Appl., 2(4), pp.333~371 (2000)
  20. G. Hinsen, "Irregular sampling of bandlimited Lp-functions", J. Approx. Theory, 72(3), pp.346~364 (1993)
  21. D. Jagerman, "Bounds for truncation error of the sampling expansion", SIAM J. Appl. Math., 14, pp.714~723 (1966)
  22. D. Jagerman, "Some general aspects of the sampling theorem", IRE Trans. Inform. Theory, 2, pp.139~146 (1956)
  23. X. M. Li, "Uniform bounds for sampling expansions", J. Approx. Theory, 93(1), pp.100~113 (1998)
  24. J. Lund, "Sinc Methods for Quadrature and Differential Equations" (1992), SIAM
  25. H. Minc, "Some inequalities involving (r!)1", r, 1964, pp.14, 41~46
  26. R. Paley, "Fourier Transforms in the Complex Domain", Amer. Math. Soc. Colloq. Publ, 19 (1934)
  27. H. S. Piper, Jr., "Bounds for truncation error in sampling expansios of finite energy band-limited signals", IEEE Trans. Inform. Theory, IT-21, pp.482~485 (1975)
  28. W. Splettst¨osser, "On approximation by the interpolating series of G. Valiron, Funct", Approx. Comment. Math., 11, pp.39~56 (1981)
  29. F. Stenger, "Numerical methods based on Whittaker cardinal, or sinc functions", SIAM Rev., 23(2), pp.165~224 (1981)
  30. F. Stenger, "Numerical Methods Based on Sinc and Analytic Functions" (1993), Springer-Verlag
  31. J. J. Voss, "Irregul¨ares Abtasten: Fehleranalyse, Anwendungen und Erweiterungen", 박사, pp.1999
  32. K. Yao, "On truncation error bounds for sampling representations of band-limited signals", IEEE Trans. Aerospace Electronic Syst., AES-2, pp.640~647 (1966)

이 간행물의 다른 논문 (14건)

ON MIXED TWO-TERM EXPONENTIAL SUMSZhang Tianpingpp. 1107-1122EIGENVALUE PROBLEM OF BIHARMONIC EQUATION WITH HARDY POTENTIALYangxin Yao, Shaotong He, Qingtang Supp. 1123-1135ON THE GOODNESS OF FIT TEST FOR DISCRETELY OBSERVED SAMPLE FROM DIFFUSION PROCESSES: DIVERGENCE MEASURE APPROACH이상열pp. 1137-1146SPLITTING TYPE, GLOBAL SECTIONS AND CHERN CLASSES FOR TORSION FREE SHEAVES ON PNCristina Bertone, Margherita Roggeropp. 1147-1165HIGHER WEIGHTS AND GENERALIZED MDS CODES한성휴, Steven T. Doughertypp. 1167-1182
원문 보기