Computing the Singular Values of 2-by-2 Complex Matrices
نویسندگان
چکیده
The singular value decomposition (SVD) of a 2-by-2 complex matrix does not occur as frequently as that of a 2-by-2 real upper triangular matrix. The commonly used QR method for SVD consists of two stages. In the first stage, a matrix is reduced to bidiagonal form using, say, Householder transformations on both sides. In the second stage, the bidiagonal matrix resulted from the first stage is diagonalized using QR iterations, where we deal with the SVDs of 2-by-2 blocks. Since the first stage, we can assume the 2-by-2 blocks real and upper triangular. However, in Jacobi methods, which are suitable for parallel computing, we have to deal with the SVD of 2-by-2 complex matrix if the original matrix is complex. Our algorithm consists of two stages. The first stage reduces B to real and upper triangular:
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