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This paper focuses on algorithms for the truncated Takagi factorization of complex symmetric matrices. The problem is formulated as a Riemannian optimization problem on a complex Stiefel manifold and then is converted into a real Riemannian ...

In this work, we consider the Takagi factorization of a matrix valued function depending on parameters. We give smoothness and genericity results and pay particular attention to the concerns caused by having either a singular value equal to 0 or multiple ...

This paper is devoted to the computation of rank-one decomposition of complex symmetric tensors. Based on the Takagi factorization of complex symmetric matrices, we derive algorithm for computing the partial orthogonal rank-one decomposition of complex ...

An algorithm for computing the singular value decomposition of normal matrices using intermediate complex symmetric matrices is proposed. This algorithm, as most eigenvalue and singular value algorithms, consists of two steps. It is based on combining ...

We describe a simple implementation of the Takagi factorization of symmetric matrices A = U U T with unitary U and diagonal 0 in terms of the square root of an auxiliary unitary matrix and the singular value decomposition of A. The method is based on an ...

Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues ...

The linear BSS problem can be solved under certain conditions via a joint diagonalization approach of only two matrices. Algebraic solutions, i.e. solutions that only involve eigenvalue decompositions or singular value decompositions, are of particular ...

The classical singular value decomposition for a matrix A@?C^m^x^n is a canonical form for A that also displays the eigenvalues of the Hermitian matrices AA^* and A^*A. In this paper, we develop a corresponding decomposition for A that provides the ...

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 ...