A hyperbolic tangent identity and the geometry of Padé sign function iterations

@article{Kenney1994AHT,
  title={A hyperbolic tangent identity and the geometry of Pad{\'e} sign function iterations},
  author={Charles S. Kenney and Alan J. Laub},
  journal={Numerical Algorithms},
  year={1994},
  volume={7},
  pages={111-128}
}
The rational iterations obtained from certain Padé approximations associated with computing the matrix sign function are shown to be equivalent to iterations involving the hyperbolic tangent and its inverse. Using this equivalent formulation many results about these Padé iterations, such as global convergence, the semi-group property under composition, and explicit partial fraction decompositions can be obtained easily. In the second part of the paper it is shown that the behavior of points… CONTINUE READING

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