Structured Numerical Linear Algebra Problems: Analysis, Algorithms, and Applications location:Cortona, Italy date:15-19 September 2008
In this talk we propose an alternative method for computing the singular values and vectors of normal matrices will be proposed. The standard way of computing all singular values of an arbitrary matrix consists of two phases. Initially the
matrix is transformed to bidiagonal form in O(n^3)
operations. Thereafter a QR-like method is applied onto the
bidiagonal matrix for computing its singular values, where each iterate costs O(n).
The method proposed in this paper consists of two parts also. An initial reduction to complex symmetric tridiagonal form of O(n^3) is performed, followed by a known QR-like method for computing the Takagi factorization.
Both an iterative manner based on Krylov sequences as a direct manner via Householder transformations, for transforming the normal matrix are presented. Some other relations such as the connection with a unitary complex symmetric factorizations are deduced.