An algorithm to compute the polar decomposition of a 3 x 3 matrix

作者：Higham Nicholas J; Noferini Vanni^*

来源：Numerical Algorithms, 2016, 73(2): 349-369.

DOI：10.1007/s11075-016-0098-7

• Polar decomposition
• 3 x 3 matrix
• Singular value decomposition
• Numerical stability
• Quaternions

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.

• 出版日期2016-10