On the convergence of Newton’s method for computing the matrix \(p\)-th root. (Chinese. English summary) Zbl 1413.65144

Ling, Yonghui

J. Zhejiang Norm. Univ., Nat. Sci. 40, No. 4, 366-372 (2017).

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)

Keywords:

matrix \(p\)-th root; principal \(p\)-th root; Newton’s method; convergence