THE INVERSE EIGENPROBLEM WITH RANK-ONE UPDATING AND ITS STABLITY

Let ∑, Г be two n-by-n diagonal matrices with σi,γi as their diagonals. For the inverse eigenvalue problem: look for y∈Rn such that Г + yyT is similar to ∑, we prove thatu also the sufficient condition for the solvability of this inverse problem. Its solution (set) is given explicitly. In some case, the problem is unstable. But we prove that the sums of the square of some contigious components keep stable, i.e., small sum keeps small, large sum has a small relative perturbation, see Theorem 3.     

A NOTE ON SENSITIVITY ANALYSIS OF SHAPE-FROM-MOMENTS

The shape-from-moments problem is to reconstruct a planar polygon from a set of its complex moments. To reconstruct a polygon means to estimate the vertices and the ordering of the vertices. We notice that some coefficients are very important in finding out the ordering of the vertices. We introduce sensitive factors for the coefficients and use it to analyze sensitivity. These factors are also useful for the sensitivity of the vertices.