$AB$-algorithm and its application for solving matrix square roots

Matthew M. Lin Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan. Chun-Yueh, Chiang Center for General Education, National Formosa University, Huwei 632, Taiwan.

Numerical Analysis and Scientific Computing mathscidoc:1609.25010

2016.9
This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a discrete-type flow depending only on the initial matrix pencil. Via this recursion relationship, we propose an accelerated iterative method to compute the stable subspace and use it to provide a theoretical result to solve the principal square root of a given matrix, both nonsingular and singular. We show that this method can not only find out the matrix square root, but also construct an iterative approach which converges to the square root with any desired order.
Stable subspace,Sherman Morrison Woodbury formula,Square root,Accelerated iterative method,Q-superlinear convergence
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@inproceedings{matthew2016$ab$-algorithm,
  title={$AB$-algorithm and its application for solving matrix square roots},
  author={Matthew M. Lin, and Chun-Yueh, Chiang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160902131348040255609},
  year={2016},
}
Matthew M. Lin, and Chun-Yueh, Chiang. $AB$-algorithm and its application for solving matrix square roots. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160902131348040255609.
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