Hyperbolic householder transforms
SIAM Journal on Matrix Analysis and Applications
Numerical methods for inverse singular value problems3
SIAM Journal on Numerical Analysis
SIAM Review
Applied Numerical Mathematics
Parameterized inverse singular value problem for anti-bisymmetric matrices
Numerical Algorithms
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In this paper the solution of an inverse singular value problem is considered. First the decomposition of a real square matrix A = UΣV is introduced, where U and V are real square matrices orthogonal with respect to a particular inner product defined through a real diagonal matrix G of order n having all the elements equal to ±1, and Σ is a real diagonal matrix with nonnegative elements, called G-singular values. When G is the identity matrix this decomposition is the usual SVD and Σ is the diagonal matrix of singular values. Given a set {σ1,..., σn} of n real positive numbers we consider the problem to find a real matrix A having them as G-singular values. Neglecting theoretical aspects of the problem, we discuss only an algorithmic issue, trying to apply a Newton type algorithm already considered for the usual inverse singular value problem.