A Study of Algorithms for the p th Root of Matrix

Langote Ulhas Baban; Dr. Mulay Prashant P.1

1

Publication Date: 2024/10/14

Abstract: Some results for Pth root of square matrix are revived. It shows that matrix sign function and Wiener- Hopf factorization plays important role in Pth root of matrix. Some new algorithms for computing P th root numerically can design by these results. We can analyze Stability properties of iterative methods for convergence.

Keywords: P th Root Of Matrix, Matrix Sign Function, Newton’s Method, Cyclic Reduction, Wiener – Hopf Factorization, Graeffe- Iteration, Laurent Polynomial.

DOI: https://doi.org/10.38124/ijisrt/IJISRT24SEP1314

PDF: https://ijirst.demo4.arinfotech.co/assets/upload/files/IJISRT24SEP1314.pdf

REFERENCES

  1. P. Benner, R. Byers, V. Mehrmann and H. Xu, A unified deflating subspace approach for classes of polynomial and rational matrix equations, Preprint SFB393/00-05, Zentrum für Technomathematik, Universität Bremen, Bremen, Germany (January 2000).
  2. M.A. Hasan, J.A.K. Hasan and L. Scharenroich, New integral representations and algorithms for computing nth roots and the matrix sector function of nonsingular complex matrices, in: Proc. of the 39th IEEE Conf. on Decision and Control, Sydney, Australia (2000) pp. 4247–4252.
  3. N.J. Higham, Newton’s method for the matrix square root, Math. Comp. 46(174) (1986) 537–549.
  4. W.D. Hoskins and D.J. Walton, A faster, more stable method for computing the pth roots of positive definite matrices, Linear Algebra Appl. 26 (1979) 139–163.       
  5. L.-S. Shieh, Y.T. Tsay and R.E. Yates, Computation of the principal nth roots of complex matrices, IEEE Trans. Automat. Control 30(6) (1985) 606–608.
  6. M.I. Smith, A Schur algorithm for computing matrix pth roots, SIAM J. Matrix Anal. Appl. 24(4) (2003) 971–989.
  7. J.S.H. Tsai, L.S. Shieh and R.E. Yates, Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix sector function, Comput. Math. Appl. 15(11) (1988) 903–913.
  8. Y.T. Tsay, L.S. Shieh and J.S.H. Tsai, A fast method for computing the principal nth roots of complex matrices, Linear Algebra Appl. 76 (1986) 205–221.