= Boundary-locus test for multistep A-stability
{title2=$z(\theta)=\rho(e^{i\theta})/\sigma(e^{i\theta})$}
A unit-modulus amplification root of a <linear multistep method> puts its test-equation parameter on this boundary locus, except when numerator and denominator both vanish. If the locus avoids the open left half-plane, the leading coefficient never vanishes there and the roots are initially inside the disk at one point there, continuity keeps them inside throughout that connected region. Checking <zero-stability>, imaginary-axis roots and common polynomial factors is still necessary. A boundary plot alone is not a proof of <A-stability>.
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