A Family of Rational Iterations and Its Application to the Computation of the Matrix pth Root

2009 ◽  
Vol 30 (4) ◽  
pp. 1445-1462 ◽  
Author(s):  
Bruno Iannazzo
Keyword(s):  
The Matrix ◽  
Matrix Pth Root

scholarly journals On High-Order Iterative Schemes for the Matrix pth Root Avoiding the Use of Inverses

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 144
Author(s):  
Sergio Amat ◽  
Sonia Busquier ◽  
Miguel Ángel Hernández-Verón ◽  
Ángel Alberto Magreñán
Keyword(s):  
Iterative Methods ◽  
Computational Cost ◽  
Good Alternative ◽  
High Order ◽  
Matrix Inverse ◽  
Numerical Examples ◽  
Iterative Schemes ◽  
The Matrix ◽  
Matrix Pth Root

This paper is devoted to the approximation of matrix pth roots. We present and analyze a family of algorithms free of inverses. The method is a combination of two families of iterative methods. The first one gives an approximation of the matrix inverse. The second family computes, using the first method, an approximation of the matrix pth root. We analyze the computational cost and the convergence of this family of methods. Finally, we introduce several numerical examples in order to check the performance of this combination of schemes. We conclude that the method without inverse emerges as a good alternative since a similar numerical behavior with smaller computational cost is obtained.

Algorithms for the matrix pth root

2005 ◽  
Vol 39 (4) ◽  
pp. 349-378 ◽  
Author(s):  
Dario A. Bini ◽  
Nicholas J. Higham ◽  
Beatrice Meini
Keyword(s):  
The Matrix ◽  
Matrix Pth Root
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