In Jacobi SVD algorithm as given here every pair of columns of the matrix is orthogonalized until convergence. I want to know that how does the order of selection of the pair of columns affect the convergence and correctness of the algorithm.
The Jacobi rotation of one pair interferes with rotation of another pair. I want to know which order is the best for converging the algorithm in the minimum number of steps. And is the correctness of the algorithm dependent on the order of selection of columns.