Singular value decomposition for complex matrices using two-sided Jacobi method

The two-sided Jacobi method for singular value decomposition (SVD) has the advantage of obtaining singular vectors quickly and accurately. In previous research, fast and accurate implementations of the two-sided Jacobi method have been achieved for real matrices. In this study, we implemented SVD for complex matrices using the two-sided Jacobi method. In SVD, given rectangular matrices can be converted into upper-triangular matrices by conducting QR decomposition as a preprocessing step. Then, the upper-triangular matrices are decomposed. In the case where the given matrices are complex, the upper-triangular matrices are complex. Two implementations are proposed: the first requires SVD for complex matrices, whereas the second requires SVD for only real matrices.