Frame completion with prescribed norms via alternating projection method.

Given a finite sequence of vectors in a finite dimensional Hilbert space, we present a method to obtain a tight frame by appending some vectors with prescribed norms. The approach, based on the alternating projection technique, is an iterative process. Von Neumann trace inequality and the polar decomposition of the matrix are employed to derive the method. The approach can be easily implemented and is numerically stable. The local convergence of the approach is achieved. Numerical examples are given to show the performance of the method. [ABSTRACT FROM AUTHOR]