Two numerical methods - one continuous and the other discrete - are proposed
for solving inverse singular value problems. The first method consists of solving an
ordinary differential equation obtained from an explicit calculation of the projected
gradient of a certain objective function. The second method generalizes an iterative
process proposed originally by Friedland et al. for solving inverse eigenvalue problems.
With the geometry understood from the first method it is shown that the
second method (also, the method proposed by Friedland et al. for inverse eigenvalue
problems ) is a variation of the Newton method. While the continuous method is
expected to converge globally at a slower rate (in finding a stationary point of the
objective function), the discrete method is proved to converge locally at a quadratic
rate (if there is a solution). Some numerical examples are presented.