On the stability of rational approximations to the cosine with only imaginary poles
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Letr(z) be a rational approximation to cosz with only imaginary poles ±iγ 1 −1/2 , ±iγ 2 −1/2 , ..., ±iγ m −1/2 such that |cozz −r(z)| ≤C|z|2m+2 as |z| → 0. If the degree of the numerator ofr(z) is less than or equal to 2m andγi ≥m/4,i=1, ...,m, then we show that |r(z)|≦1 for all realz.
AMS Subject Classification65L07
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