No. 37 (254), issue 10Pages 99 - 107


O.L. Ibryaeva
A new algorithm for calculating a Pade approximant is proposed. The algorithm is based on the choice of the Pade approximant's denominator of least degree. It is shown that the new algorithm does not lead to the appearance of the Froissart doublets in contrast to available procedures for calculating Pade approximants in Maple and Mathematica.
Full text
Pade approximant, Froissart doublets, Pade - Laplace method, ill-posed problem.
1. Baker G.A. Pade Approximants. Cambridge, University Press, 1996.
2. Cabay S., Choi D.K. Algebraic computations of scaled Pade fractions. SIAM J. on Computing, 1986, v. 15, no. 1, pp. 243 - 270.
3. Geddes K.O. Symbolic computation of Pade approximants ACM Transactions on Mathematical Software, 1979, v. 5, no. 2, pp. 218 - 233.
4. Adukov V.M. The problem of Pade approximation as the Riemann boundary problem [Zadacha approksimatsii Pade kak kraevaya zadacha Rimana]. Vestsi NAN Belarusi. Seriya Fiziko-matem. nauk [Proceedings of NAS of Belarus. Series of physical and mathematical sciences], 2004, no. 4, pp. 55 - 61.
5. Schestakov A.L., Adukov V.M., Ibryaeva O.L., Semenov A.S. On Froissart doublets in Pade - Laplace method [O dupletakh Fruassara v metode Pade - Laplasa]. Tezisy dokladov mezhdunarodnoi conferensii 'Sistemy compyuternoi matematiki i ikh prilozheniya' , [Theses of reports of the International Conference ' Systems of computer mathematics and their applications'], Smolensk, 2011, pp. 257 - 259.
6. Claverie P., Denis A., Yeramian E. The representation of functions through the combined use of integral transforms and Pade approximants: Pade - Laplace analysis of functions as sums of exponentials Computer Physics Reports, 1989, no. 9, pp. 247 - 299.
7. Golub G.H., Van Loan C.F. Matrix Computations. Baltimore, University Press, 1989, pp. 557 - 558.