Revisiting the stability of computing the roots of a quadratic polynomial

Mastronardi Nicola; Van Dooren Paul

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arXiv · 1409.8072

Revisiting the stability of computing the roots of a quadratic polynomial

Mastronardi Nicola·Van Dooren Paul

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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.

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Mastronardi Nicola, Van Dooren Paul. 2014-09-29. Revisiting the stability of computing the roots of a quadratic polynomial. https://arxiv.org/abs/1409.8072

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