A Divide-and-Conquer Method for the Takagi Factorization

This paper presents a divide-and-conquer method for computing the symmetric singular value decomposition, or Takagi factorization, of a complex symmetric and tridiagonal matrix. An analysis of accuracy shows that our method produces accurate Takagi values and orthogonal Takagi vectors. Our preliminary numerical experiments have confirmed our analysis and demonstrated that our divide-and-conquer method is much more efficient than the implicit QR method even for moderately large matrices.