Abstract
This paper presents an O ( n 2 log n ) algorithm for computing the symmetric singular value decomposition of square Hankel matrices of order n, in contrast with existing O ( n 3 ) SVD algorithms. The algorithm consists of two stages: first, a complex square Hankel matrix is reduced to a complex symmetric tridiagonal matrix using the block Lanczos method in O ( n 2 log n ) flops; Second, the singular values and singular vectors of the symmetric tridiagonal matrix resulted from the first stage are computed in O ( n 2 ) flops. The singular vector matrix is given in the form of a product of three or two unitary matrices. The performance of our algorithm is demonstrated by comparing it with the SVD subroutines in Matlab and LAPACK.
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