Sequential and parallel computation for matrix relative primeness, stability and inertia problems

We present sequential and parallel algorithms for two important linear algebra problems in control theory, namely, determining relative primeness and the number of common eigenvalues between two matrices and inertia and stability of a matrix. Sequentially, these algorithms are more efficient than the existing ones and in parallel they can be implemented in almost linear time step using at most O(n2) processors. An important and desirable feature of these algorithms is that they comprise of basic linear algebraic operations only for which there already exist effective parallel algorithms.