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- W1682300399 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 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." @default.
- W1682300399 created "2016-06-24" @default.
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- W1682300399 date "2014-09-29" @default.
- W1682300399 modified "2023-09-27" @default.
- W1682300399 title "Revisiting the stability of computing the roots of a quadratic polynomial" @default.
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