95
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A novel approach to the theory of Padé approximants

Pages 15-27 | Published online: 21 Jan 2013

References

  • Aitken A C Determinants and Matrices, 9th Ed., Oliver and Boyd (1959)
  • Athorne C The representation theory of Padé approximants, J. Phys. A: Math. Gen. 37 (2004), 7699–7710
  • Athorne C Algebraic Hirota Derivatives, Phys. Lett. A 256 (1999), 20–24
  • Athorne C Invariant theory and Hirota Derivatives, Glasg. Math. J. 43A (2001), 1–8
  • Athorne C Algebraic Hirota Maps, NATO ARW proceedings, Elba 2002
  • Berezinski The long history of continued fractions and Padé approximants, in Padé Approximation and its Applications, pp. 1–27, Amsterdam 1980, Ed. M.G. de Bruin and H. van Rossum, Lecture Notes in Mathematics 888, Springer 1981
  • Boyer C P Miller W Jnr A Relationship between Lie Theory anf Continued Fraction Expansions for Special Functions, in Padé and Rational Approximation, Ed. Saff, E.B. and Varga, R.S., (1977) Academic Press
  • Cuyt A A M The QD-algorithm and Multivariate Padé-Approximants, Numer. Math. 42 (1983) pp. 259–269
  • Frobenius G Stickelberger L. Über die Addition und Multiplication der elliptischen Functionen, Jour. für die reine und angewandte Mathematik 88 (1880) pp. 146–184
  • Gragg W B The Pade Table and Its Relation to Certain Algorithms of Numerical Analysis, SIAM Review, 14 (1972), 1–62
  • Hilbert D Theory of Algebraic Invariants, CUP (1993)
  • Hirota R Bilinearization of soliton equations, J. Phys. Soc. Japan, 51 (1982) pp. 323–331
  • Papageorgiou V Grammaticos B Ramani A Integrable lattices and convergence acceleration algorithms Phys. Lett. A179 (1993), 111–115
  • Wynn P Upon systems of recursions which obtain among the quotients of the Padé table, Numer. Math. 8 (1966) pp. 246–269

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.