Solution methods to the nearest rotation matrix problem in Double-struck capital R3: A comparative survey

Nowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed-form methods are as robust as the SVD, but significantly faster and more accurate.

Automated summary

Nowadays, the Singular Value Decomposition (SVD) is commonly used for solving the nearest rotation matrix problem. However, there are many other methods available for the 3D case. This article reviews and proposes alternative methods, and presents a comparative analysis to determine their computational costs and error performances. The analysis concludes that some algebraic closed-form methods are as robust as SVD, but faster and more accurate.