A divide-and-conquer method for the Takagi factorization. (English) Zbl 1159.65321
Summary: 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.
MSC:
65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
65F25 | Orthogonalization in numerical linear algebra |
65F50 | Computational methods for sparse matrices |