Proposed Preprocessing for High–Performance Complex Singular Value Decomposition

The computation of singular value decomposition by the two-sided Jacobi method has the advantage of obtaining sin-gular vectors fast and accurately. Prior research has achieved fast and accurate implementations of the two-sided Jacobi method for both real and complex matrices. One problem, however, is the large amount of operations and long execution time for complex matrices. To solve this problem, as a preprocessing, a singular value decomposition of a complex matrix is converted into a singular value decomposition of a real upper bidiagonal matrix. In this paper, we implement the preprocessing and confirm that it is faster than the direct treatment of complex matrices from the two-sided Jacobi method.