Araştırma Makalesi
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Yıl 2019, , 135 - 153, 27.06.2019

François Dubeau

https://doi.org/10.33434/cams.512796

Öz

Kaynakça

  • [1] P. J. Davis, Interpolation and Approximation, Dover, N.Y., 1975.
  • [2] A. S. Househoulder, Principles of Numerical Analysis, McGraw Hill, Columbus, N.Y., 1953.
  • [3] D. Kincaid, W. Cheney, Numerical Analysis, Brooks/Cole Pub. Co., Cal., 1991.
  • [4] A. Ralston, A First Course in Numerical Analysis, McGraw-Hill, N.Y., 1965.
  • [5] N. Macon, A. Spitzbart, Inverses of Vandermonde matrices, Amer. Math. Monthly, 65(2) (1958), 95-100. http://dx.doi.org/10.2307/2308881
  • [6] E. Asplund, L. Bungart, A First Course in Integration, Holt, Rinehart and Winston, N.Y., 1966.
  • [7] L. L. Schumaker, Spline Functions Basic Theory, Wiley, N.Y., 1981.
  • [8] G. Peano, Resto nelle formule di quadratura espresso con un integrale definito, Atti. Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Nat., Serie 5, 22(I) (1913), 562-569.
  • [9] R. von Mises, U¨ ber allgemeine quadraturformeln, J. Reine Angew. Math., 174 (1935), 56-67; reprinted in Selected Papers of Richard von Mises, Vol. 1, 559-574, American Mathematical Society, Providence, R.I., 1963.
  • [10] A. Ghizzetti, A. Ossicini, Quadrature Formulae, Academic Press, N.Y., 1970.
  • [11] F. Dubeau, Revisited optimal error bounds for interpolatory integration rules, Adv. Numer. Anal., 2016 (2016), Article ID 3170595, 8 pages, http://dx.doi.org/10.1155/2016/3170595.
  • [12] F. Dubeau, The method of undetermined coefficients: general approach and optimal error bounds, J. Math. Anal., 5(4) (2014), 1-11.
  • [13] J. S. C. Prentice, Truncation and roundoff errors in three-point approximations of first and second derivatives, Appl. Math. Comput., 217 (2011), 4576-4581. http://dx.doi.org/10.1016/j.amc.2010.11.008
  • [14] N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd Ed., SIAM, Philadelphia, PN, 2002. http://dx.doi.org/10.1137/1.9780898718027

Standard and Corrected Numerical Differentiation Formulae

Yıl 2019, , 135 - 153, 27.06.2019

François Dubeau

https://doi.org/10.33434/cams.512796

Öz

Standard numerical differentiation rules that might be established by the method of undetermined coefficients are revisited. Best truncation error bounds are established by a direct method and by the method of integration by parts "backwards". A new method to increase the order of the truncation error using a primitive is presented. This approach leads to corrected numerical differentiation rules. Differentiation formulae and numerical tests are presented.

Anahtar Kelimeler

Absolutely continuous function Method of undetermined coefficients Numerical differentiation rules Peano kernel Taylor's expansion

Kaynakça

  • [1] P. J. Davis, Interpolation and Approximation, Dover, N.Y., 1975.
  • [2] A. S. Househoulder, Principles of Numerical Analysis, McGraw Hill, Columbus, N.Y., 1953.
  • [3] D. Kincaid, W. Cheney, Numerical Analysis, Brooks/Cole Pub. Co., Cal., 1991.
  • [4] A. Ralston, A First Course in Numerical Analysis, McGraw-Hill, N.Y., 1965.
  • [5] N. Macon, A. Spitzbart, Inverses of Vandermonde matrices, Amer. Math. Monthly, 65(2) (1958), 95-100. http://dx.doi.org/10.2307/2308881
  • [6] E. Asplund, L. Bungart, A First Course in Integration, Holt, Rinehart and Winston, N.Y., 1966.
  • [7] L. L. Schumaker, Spline Functions Basic Theory, Wiley, N.Y., 1981.
  • [8] G. Peano, Resto nelle formule di quadratura espresso con un integrale definito, Atti. Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Nat., Serie 5, 22(I) (1913), 562-569.
  • [9] R. von Mises, U¨ ber allgemeine quadraturformeln, J. Reine Angew. Math., 174 (1935), 56-67; reprinted in Selected Papers of Richard von Mises, Vol. 1, 559-574, American Mathematical Society, Providence, R.I., 1963.
  • [10] A. Ghizzetti, A. Ossicini, Quadrature Formulae, Academic Press, N.Y., 1970.
  • [11] F. Dubeau, Revisited optimal error bounds for interpolatory integration rules, Adv. Numer. Anal., 2016 (2016), Article ID 3170595, 8 pages, http://dx.doi.org/10.1155/2016/3170595.
  • [12] F. Dubeau, The method of undetermined coefficients: general approach and optimal error bounds, J. Math. Anal., 5(4) (2014), 1-11.
  • [13] J. S. C. Prentice, Truncation and roundoff errors in three-point approximations of first and second derivatives, Appl. Math. Comput., 217 (2011), 4576-4581. http://dx.doi.org/10.1016/j.amc.2010.11.008
  • [14] N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd Ed., SIAM, Philadelphia, PN, 2002. http://dx.doi.org/10.1137/1.9780898718027
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

François Dubeau 0000-0002-2956-3208

Yayımlanma Tarihi 27 Haziran 2019
Gönderilme Tarihi 14 Ocak 2019
Kabul Tarihi 12 Nisan 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Dubeau, F. (2019). Standard and Corrected Numerical Differentiation Formulae. Communications in Advanced Mathematical Sciences, 2(2), 135-153. https://doi.org/10.33434/cams.512796
AMA Dubeau F. Standard and Corrected Numerical Differentiation Formulae. Communications in Advanced Mathematical Sciences. Haziran 2019;2(2):135-153. doi:10.33434/cams.512796
Chicago Dubeau, François. “Standard and Corrected Numerical Differentiation Formulae”. Communications in Advanced Mathematical Sciences 2, sy. 2 (Haziran 2019): 135-53. https://doi.org/10.33434/cams.512796.
EndNote Dubeau F (01 Haziran 2019) Standard and Corrected Numerical Differentiation Formulae. Communications in Advanced Mathematical Sciences 2 2 135–153.
IEEE F. Dubeau, “Standard and Corrected Numerical Differentiation Formulae”, Communications in Advanced Mathematical Sciences, c. 2, sy. 2, ss. 135–153, 2019, doi: 10.33434/cams.512796.
ISNAD Dubeau, François. “Standard and Corrected Numerical Differentiation Formulae”. Communications in Advanced Mathematical Sciences 2/2 (Haziran 2019), 135-153. https://doi.org/10.33434/cams.512796.
JAMA Dubeau F. Standard and Corrected Numerical Differentiation Formulae. Communications in Advanced Mathematical Sciences. 2019;2:135–153.
MLA Dubeau, François. “Standard and Corrected Numerical Differentiation Formulae”. Communications in Advanced Mathematical Sciences, c. 2, sy. 2, 2019, ss. 135-53, doi:10.33434/cams.512796.
Vancouver Dubeau F. Standard and Corrected Numerical Differentiation Formulae. Communications in Advanced Mathematical Sciences. 2019;2(2):135-53.

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