Higham, Nicholas J and Noferini, Vanni (2016) An algorithm to compute the polar decomposition of a 3 × 3 matrix. Numerical Algorithms, 73 (2). pp. 349-369. DOI https://doi.org/10.1007/s11075-016-0098-7
Higham, Nicholas J and Noferini, Vanni (2016) An algorithm to compute the polar decomposition of a 3 × 3 matrix. Numerical Algorithms, 73 (2). pp. 349-369. DOI https://doi.org/10.1007/s11075-016-0098-7
Higham, Nicholas J and Noferini, Vanni (2016) An algorithm to compute the polar decomposition of a 3 × 3 matrix. Numerical Algorithms, 73 (2). pp. 349-369. DOI https://doi.org/10.1007/s11075-016-0098-7
Abstract
We propose an algorithm for computing the polar decomposition of a 3 × 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: | Article |
|---|---|
| Uncontrolled Keywords: | Polar decomposition; 3 x 3 matrix; Singular value decomposition; Numerical stability; Quaternions |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 27 Jun 2016 10:36 |
| Last Modified: | 04 Dec 2024 06:31 |
| URI: | http://repository.essex.ac.uk/id/eprint/17058 |
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