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arXiv · 2609.27520

Component-wise accurate fixed point iterations for computing the square root of a singular M-matrix

Dario Andrea Bini·Bruno Iannazzo·Beatrice Meini·Jie Meng
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Abstract

We analyze two fixed-point iterations for computing the principal square root of an M-matrix $A$. Although these iterations, with customary initialization, converge sublinearly when $A$ is a singular M-matrix, we show that, under suitable mild conditions on the initial approximation, the convergence is linear. Moreover, we provide component-wise accurate versions of these iterations, which allow us to approximate the principal square root with a component-wise relative error uniformly bounded by a small multiple of the machine precision. Numerical experiments demonstrating the effectiveness of the proposed algorithms for certain classes of problems are presented.

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Dario Andrea Bini, Bruno Iannazzo, Beatrice Meini, Jie Meng. 2026-09-23. Component-wise accurate fixed point iterations for computing the square root of a singular M-matrix. https://arxiv.org/abs/2609.27520

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