## 2015.66: An algorithm to compute the polar decomposition of a 3x3 matrix

2015.66:
Nicholas J Higham and Vanni Noferini
(2015)
*An algorithm to compute the polar decomposition of a 3x3 matrix.*

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## Abstract

We propose an algorithm for computing the polar decomposition of a 3 x 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our algorithm is numerically reliable and requires fewer arithmetic operations than the alternative of computing the polar decomposition via the singular value decomposition.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | Polar decomposition, 3x3 matrix, singular value decomposition, numerical stability, quaternions |

Subjects: | MSC 2000 > 11 Number theory MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2015.66 |

Deposited By: | Dr V Noferini |

Deposited On: | 31 July 2015 |

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