Revisiting the stability of computing the roots of a quadratic polynomial

الأصل · EN

We show in this paper that the roots x₁ and x₂ of a scalar quadratic polynomial ax²+bx+c=0 with real or complex coefficients a, b c can be computed in a element-wise mixed stable manner, measured in a relative sense. We also show that this is a stronger property than norm-wise backward stability, but weaker than element-wise backward stability. We finally show that there does not exist any method that can compute the roots in an element-wise backward stable sense, which is also illustrated by some numerical experiments.