The problem of determining the eigenvalues of a given matrix A is one of long-standing and wide application in many areas of science and engineering. By contrast, the problem of determining all or some of the entries of A fron spectral information is a new subject which has only recently become an active area of research. We quote Z. Bohte [2], (p. 385, 1967): "For the numerical solution of this problem a number of techniques have been used without sufficient theoretical consideration. We believe the problem has not attracted the attention of the mathematicians yet".