Abstract
We show in this paper that the roots $x_1$ and $x_2$ of a scalar quadratic polynomial $ax^2 + bx + c = 0$
with real or complex coefficients $a, b, c$ can be computed in an 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.
Anno
2015
Autori IAC
Tipo pubblicazione
Altri Autori
Nicola Mastronardi, Paul Van Dooren
Editore
Kent State University,
Rivista
Electronic transactions on numerical analysis