How to solve multiplicative inverse eigenvalue problem using Matlab

(Fisher and Fuller Theorem) Let A be an n x n real matrix all of whose leading principal minors are positive. Then there is an n x n positive diagonal matrix D such that all the roots of DA are positive and simple.

Reference: M. E. Fisher and A. T. Fuller, On the stabilization of matrices and the convergence of linear iterative processes, Proc. Cambridge Philos. Soc. 54 (1958), 417-425.