Rational approximations for the cosine function; P-acceptability and order. (English) Zbl 0785.65093

The paper deals with rational approximations \(R_{nm}(z^ 2)\) (with the numerator of the degree \(n\) and the denominator of the degree \(m\)) of the function \(\cos z\). It is proved that the order of accuracy of a \(P\)- acceptable \(R_{nm}\) (i.e. \(| R_{nm}(\nu^ 2)| < 1\) for all \(\nu > 0\)) cannot exceed \(2m\). Further, if the poles of \(R_{nm}(z^ 2)\) are pure-imaginary, then the maximum attainable order is \(2n+2\) for \(m\geq 1\).
Reviewer: M.Bartušek (Brno)


65L20 Stability and convergence of numerical methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
41A20 Approximation by rational functions
65D20 Computation of special functions and constants, construction of tables
34A34 Nonlinear ordinary differential equations and systems
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