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Rational approximants defined from double power series


Author: J. S. R. Chisholm
Journal: Math. Comp. 27 (1973), 841-848
MSC: Primary 41A20
DOI: https://doi.org/10.1090/S0025-5718-1973-0382928-6
MathSciNet review: 0382928
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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.


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DOI: https://doi.org/10.1090/S0025-5718-1973-0382928-6
Keywords: Approximation theory, rational approximation, double series, Padé approximants, invariance properties
Article copyright: © Copyright 1973 American Mathematical Society