Positive Semidefinite Solution to Matrix Completion Problem and Matrix Approximation Problem

In this paper, firstly, we discuss the following matrix completion problem in the spectral norm: parallel to( [GRAPHICS] parallel to(2) < 1 subject to ( [GRAPHICS] )>= 0. The feasible condition for the above problem is established, in this case, the general positive semidefinite solution and its minimum rank are presented. Secondly, applying the result of the above problem, we also study the matrix approximation problem: parallel to A - BXB*parallel to(2) < 1 subject to A - BXB* >= 0, where A is an element of C->=(mxm), B is an element of C-mxn, and X is an element of C->=(nxn).