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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 of the algorithm.

I am working on implementing this algorithm. In my program even though I am covering every pair of columns but still with a certain order of selection of columns the algorithm doesn't converge even after thousands of iteration. But with ordering like cyclic ordering, the algorithm converges in 10-12 iterations.

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.

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