Rational approximants defined from double power series
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- by J. S. R. Chisholm PDF
- Math. Comp. 27 (1973), 841-848 Request permission
Abstract:
Rational approximants are defined from double power series in variables x and y, and it is shown that these approximants have the following properties: (i) they possess symmetry between x and y; (ii) they are in general unique; (iii) if $x = 0$ or $y = 0$, they reduce to diagonal Padé approximants; (iv) their definition is invariant under the group of transformations $x = Au/(1 - Bu),y = Av/(1 - Cv)$ with $A \ne 0$; (v) an approximant formed from the reciprocal series is the reciprocal of the corresponding original approximant. Possible variations, extensions and generalisations of these results are discussed.References
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- P. R. Graves-Morris (ed.), Padé approximants and their applications, Academic Press, London-New York, 1973. MR 0435681
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 841-848
- MSC: Primary 41A20
- DOI: https://doi.org/10.1090/S0025-5718-1973-0382928-6
- MathSciNet review: 0382928