The bidiagonal singular value decomposition and Hamiltonian mechanics. (English) Zbl 0737.65035

The authors present an algorithm to compute the singular value decomposition of a bidiagonal matrix \(B\) with an error bound depending on the relative gap. It is also shown that this algorithm computes the singular vectors as well as singular values to this accuracy. A Hamiltonian interpretation of the algorithm is also given, and differential equation methods are used to prove many of the basic facts. Numerical experiments are also presented for illustration.


65F15 Numerical computation of eigenvalues and eigenvectors of matrices
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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