Proposal and efficient implementation of multiple division divide-and-conquer algorithm for SVD

We propose a divide-and-conquer algorithm with multiple division for singular value decomposition (SVD).The algorithm turns out to be efficient for reducing the execution time in the case that the deflation occurrence rate of the input matrix is low, which is exactly the case that the standard divide-and-conquer algorithm (DC2-SVD) with division number two requires O(n 3 ) arithmetic operations.Here n is the size of the input matrix.The comparison with DC2-SVD as well as another up-to-date algorithm I-SVD is made through numerical experiment.