Higham, Nicholas J and Noferini, Vanni
(2015)
*An algorithm to compute the polar decomposition of a 3x3 matrix.*
[MIMS Preprint]

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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 2010, the AMS's Mathematics Subject Classification > 11 Number theory MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |

Depositing User: | Dr V Noferini |

Date Deposited: | 31 Jul 2015 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2352 |

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