Frame completion with prescribed norms via alternating projection method (Q1995944)

The author presents a method to construct a tight frame in a finite dimensional Hilbert space starting from a given finite sequence of vectors. More precisely, the method is a tight frame completion technique, i.e. it consists to append some vectors with prescribed norms to the original sequence. The method makes use of Von Neumann trace inequality and the polar decomposition of the matrix. It is an iterative process, based on the alternating projection technique, it is numerically stable and the local convergence of the approach is achieved. The author describes a corresponding algorithm and shows numerical examples.