Beata Laszkiewicz, Krystyna Zietak, 
"A Pade family of iterations for the matrix sector function and the matrix pth root"

A family of iterations for the sector function based on the Pade table 
of a certain  hypergeometric function is derived and investigated.
This generalizes a result of Kenney and Laub for the  sign function 
and yields a whole family of iterative methods for computing 
the  matrix $p$th root. 

It is proved that the iterations for the matrix sector function corresponding
to the main diagonal of the  Pade table preserve the structure of a group 
of automorphisms associated with a scalar product. 

The regions of  convergence of the Pade iterations for the matrix sector function 
are investigated  theoretically and experimentally. Certain  conjectures 
formulated on the regions of convergence have been verified in particular cases. 



key words:  matrix sector function, matrix root, Pade approximation, 
            rational matrix iterations, structure preserving iteration