Could anyone recommend a method for the following least squares problem:find $R \in \mathbb{R}^{3 \times 3}$ that minimizes : $\sum_{i=0}^N (Rx_i - b_i)^2 \rightarrow  min$, where $R$ is unitary (rotation) matrixI could get an approximate solution by minimizing $\sum_{i=0}^N (Ax_i - b_i)^2 \rightarrow  min$ (arbitrary $A \in \mathbb{R}^{3 \times 3}$), taking matrix $A$ and:computing SVD: $A = U \Sigma V^T$, dropping $\Sigma$ and approximating $R \approx U V^T$ computing polar decomposition: $A = U P$, dropping scale-only symmetric (and positive definite in my case) $P$ and approximating $R \approx U$I could also use QR decomposition, but it wouldn't be isometric (would depend on the choice of coordinate system).Does anyone know of a way to do this, at least approximately, but with better apprimation than the two methods above?Thanks in advance!-Sergiy
Purely rotational least squares match
linear algebra;least squares