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Rational approximants generated by the \(u\)-transform. (English) Zbl 0878.65011

Summary: Rational approximants of some functions are generated from their respective infinite power series expansions using the nonlinear sequence transform \(u\). The fidelity of the \(u\)-approximant is observed to be generally better than the standard Padé approximant except when a function has both poles and zeros. Comparison is also made between the two types of approximants in obtaining approximate closed form solutions of ordinary differential equations for both initial value and boundary value problems.

MSC:

65D20 Computation of special functions and constants, construction of tables
41A20 Approximation by rational functions
65B05 Extrapolation to the limit, deferred corrections
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