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On the convergence of Newton’s method for computing the matrix $$p$$-th root. (Chinese. English summary) Zbl 1413.65144
Summary: This paper considered the convergence region of Newton’s method for computing the principal $$p$$-th root of a matrix. We obtained a new convergence region by using the theory of complex analysis. It was shown that the Newton method converged to the principal $$p$$-th root quadratically when all the eigenvalues of the matrix located in this new region.
##### MSC:
 65F30 Other matrix algorithms (MSC2010)
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