Solving Additive Inverse Eigenvalue Problems for Symmetric Matrices by the Homotopy Method
Moody T. Chu · IMA Journal of Numerical Analysis · 1990
Additive inverse eigenvalue problems can be formulated as systems of polynomial equations. Following from recent developments in solving polynomial systems, we formulate a special homotopy function to provide a fresh proof of the classical result of Friedland. In theory our approach has the advantage of offering a globally convergent method by which all solutions, if desired, can be found systematically and independently. When the underlying matrix is symmetric and tridiagonal, we discuss how the computational tasks can be accomplished at a reasonable cost.