[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]

R. Bhatia, *Matrix Analysis* (Springer, New York, 1997).

[3]

D.A. Bini, L. Gemignani and B. Meini, Computations with infinite Toeplitz matrices and polynomials, Linear Algebra Appl. 343/344 (2002) 21–61.

[4]

D.A. Bini, L. Gemignani and B. Meini, Solving certain matrix equations by means of Toeplitz computations: Algorithms and applications, in: *Fast Algorithms for Structured Matrices: Theory and Applications*, ed. V. Olshevsky, Contemporary Mathematics, Vol. 323 (Amer. Math. Soc., Providence, RI, 2003) pp. 151–167.

[5]

D.A. Bini and B. Meini, Improved cyclic reduction for solving queueing problems, Numer. Algorithms 15(1) (1997) 57–74.

[6]

D.A. Bini and B. Meini, Non-skip-free *M*/*G*/1-type Markov chains and Laurent matrix power series, Linear Algebra Appl. 386 (2004) 187–206.

[7]

D.A. Bini and V.Y. Pan, *Polynomial and Matrix Computations*, Vol. 1: *Fundamental Algorithms* (Birkhäuser, Boston, MA, 1994).

[8]

A. Böttcher and B. Silbermann, Introduction to Large Truncated Toeplitz Matrices (Springer, New York, 1999).

[9]

B.L. Buzbee, G.H. Golub and C.W. Nielson, On direct methods for solving Poisson’s equations, SIAM J. Numer. Anal. 7(4) (1970) 627–656.

[10]

S.H. Cheng, N.J. Higham, C.S. Kenney and A.J. Laub, Approximating the logarithm of a matrix to specified accuracy, SIAM J. Matrix Anal. Appl. 22(4) (2001) 1112–1125.

[11]

P. J. Davis and P. Rabinowitz, *Methods of Numerical Integration*, 2nd ed. (Academic Press, London, 1984).

[12]

M.A. Hasan, A.A. Hasan and K.B. Ejaz, Computation of matrix *n*th roots and the matrix sector function, in: *Proc. of the 40th IEEE Conf. on Decision and Control*, Orlando, FL (2001) pp. 4057–4062.

[13]

M.A. Hasan, J.A.K. Hasan and L. Scharenroich, New integral representations and algorithms for computing *n*th 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.

[14]

N.J. Higham, The Matrix Computation Toolbox,

http://www.ma.man.ac.uk/~higham/mctoolbox.

[15]

N.J. Higham, Newton’s method for the matrix square root, Math. Comp. 46(174) (1986) 537–549.

[16]

N.J. Higham, The matrix sign decomposition and its relation to the polar decomposition, Linear Algebra Appl. 212/213 (1994) 3–20.

[17]

N.J. Higham, *Accuracy and Stability of Numerical Algorithms*, 2nd ed. (SIAM, Philadelphia, PA, 2002).

[18]

W.D. Hoskins and D.J. Walton, A faster, more stable method for computing the *p*th roots of positive definite matrices, Linear Algebra Appl. 26 (1979) 139–163.

[19]

C.S. Kenney and A.J. Laub, Condition estimates for matrix functions, SIAM J. Matrix Anal. Appl. 10(2) (1989) 191–209.

[20]

Ç.K. Koç and B. Bakkaloğlu, Halley’s method for the matrix sector function, IEEE Trans. Automat. Control 40(5) (1995) 944–949.

[21]

M.L. Mehta, *Matrix Theory: Selected Topics and Useful Results*, 2nd ed. (Hindustan Publishing, Delhi, 1989).

[22]

B. Meini, The matrix square root from a new functional perspective: Theoretical results and computational issues, Technical Report 1455, Dipartimento di Matematica, Università di Pisa (2003), to appear in SIAM J. Matrix Anal. Appl.

[23]

M.A. Ostrowski, Recherches sur la méthode de Graeffe et les zeros des polynômes et des séries de Laurent, Acta Math. 72 (1940) 99–257.

[24]

B. Philippe, An algorithm to improve nearly orthonormal sets of vectors on a vector processor, SIAM J. Algebra Discrete Methods 8(3) (1987) 396–403.

[25]

G. Schulz, Iterative Berechnung der reziproken Matrix, Z. Angew. Math. Mech. 13 (1933) 57–59.

[26]

L.-S. Shieh, Y.T. Tsay and R.E. Yates, Computation of the principal *n*th roots of complex matrices, IEEE Trans. Automat. Control 30(6) (1985) 606–608.

[27]

M.I. Smith, A Schur algorithm for computing matrix *p*th roots, SIAM J. Matrix Anal. Appl. 24(4) (2003) 971–989.

[28]

J.S.H. Tsai, L.S. Shieh and R.E. Yates, Fast and stable algorithms for computing the principal *n*th root of a complex matrix and the matrix sector function, Comput. Math. Appl. 15(11) (1988) 903–913.

[29]

Y.T. Tsay, L.S. Shieh and J.S.H. Tsai, A fast method for computing the principal *n*th roots of complex matrices, Linear Algebra Appl. 76 (1986) 205–221.