= A-stability of near-diagonal exponential Padé approximants
{c}
{title2=$n-2\le m\le n$}
For nonnegative degrees $m,n$ with $n-2\le m\le n$, the $[m/n]$ <Padé approximant> $R$ to the <exponential function> has no poles in the left half-plane and satisfies $|R(z)|\le1$ for $\operatorname{Re}z\le0$. Consequently a numerical method having that <stability function> is <A-stable>. In particular, the near-diagonal choice $[s-1/s]$ gives the <Radau IIA method> stability function, while $[s/s]$ corresponds to the <Gauss collocation method>. The theorem concerns these exponential approximants, not arbitrary rational approximations with the same degrees.
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