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.
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This work was supported by European Research Council Advanced Grant MATFUN (267526) and Engineering and Physical Sciences Research Council grant EP/I03112X/1
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Higham, N.J., Noferini, V. An algorithm to compute the polar decomposition of a 3 × 3 matrix. Numer Algor 73, 349–369 (2016). https://doi.org/10.1007/s11075-016-0098-7
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DOI: https://doi.org/10.1007/s11075-016-0098-7