A twisted factorization method for symmetric SVD of a complex symmetric tridiagonal matrix

Abstract This paper presents an O ( n 2 ) method based on the twisted factorization for computing the Takagi vectors of an n ‐by‐ n complex symmetric tridiagonal matrix with known singular values. Since the singular values can be obtained in O ( n 2 ) flops, the total cost of symmetric singular value decomposition or the Takagi factorization is O ( n 2 ) flops. An analysis shows the accuracy and orthogonality of Takagi vectors. Also, …