## 2012.26: Blocked Schur Algorithms for Computing the Matrix Square Root

2012.26:
Edvin Deadman, Nicholas J. Higham and Rui Ralha
(2012)
*Blocked Schur Algorithms for Computing the Matrix Square Root.*

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## Abstract

The Schur method for computing a matrix square root reduces the matrix to the Schur triangular form and then computes a square root of the triangular matrix. We show that by using either standard blocking or recursive blocking the computation of the square root of the triangular matrix can be made rich in matrix multiplication. Numerical experiments making appropriate use of level 3 BLAS show significant speedups over the point algorithm, both in the square root phase and in the algorithm as a whole. In parallel implementations, recursive blocking is found to provide better performance than standard blocking when the parallelism comes only from threaded BLAS, but the reverse is true when parallelism is explicitly expressed using OpenMP. The excellent numerical stability of the point algorithm is shown to be preserved by blocking. These results are extended to the real Schur method. Blocking is also shown to be effective for multiplying triangular matrices.

Item Type: | MIMS Preprint |
---|---|

Additional Information: | To appear in Springer Lecture Notes in Computer Science |

Uncontrolled Keywords: | matrix function square root Schur recursive |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2012.26 |

Deposited By: | Dr Edvin Deadman |

Deposited On: | 05 December 2012 |

### Available Versions of this Item

- Blocked Schur Algorithms for Computing the Matrix Square Root (deposited 11 March 2013)
- Blocked Schur Algorithms for Computing the Matrix Square Root (deposited 05 December 2012)
**[Currently Displayed]** - A Recursive Blocked Schur Algorithm for Computing the Matrix Square Root (deposited 30 January 2012)

- Blocked Schur Algorithms for Computing the Matrix Square Root (deposited 05 December 2012)

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