Numerical Algorithms

, Volume 39, Issue 4, pp 349–378

Algorithms for the matrix pth root


    • Dipartimento di MatematicaUniversità di Pisa
  • Nicholas J. Higham
    • Department of MathematicsUniversity of Manchester
  • Beatrice Meini
    • Dipartimento di MatematicaUniversità di Pisa

DOI: 10.1007/s11075-004-6709-8

Cite this article as:
Bini, D.A., Higham, N.J. & Meini, B. Numer Algor (2005) 39: 349. doi:10.1007/s11075-004-6709-8


New theoretical results are presented about the principal matrix pth root. In particular, we show that the pth root is related to the matrix sign function and to the Wiener–Hopf factorization, and that it can be expressed as an integral over the unit circle. These results are used in the design and analysis of several new algorithms for the numerical computation of the pth root. We also analyze the convergence and numerical stability properties of Newton’s method for the inverse pth root. Preliminary computational experiments are presented to compare the methods.


matrix pth rootmatrix sign functionWiener–Hopf factorizationNewton’s methodGraeffe iterationcyclic reductionLaurent polynomial
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© Springer 2005