论文信息 - On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem

On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem

Abstract In this paper, we give simple and elementary proofs of the two classical results of Fujiwara on the solution of the well-known Routh-Hurwitz and Schur-Cohn problems. We show that the Fujiwara matrix in each case satisfies a Lyapunov-type equation and then obtain Fujiwara's results by applying to this matrix equation some recent results on the inertia of matrices. These alternative proofs of Fujiwara's results thus establish a link between two apparently different approaches to the solution of the root-separation problem: the classical method of solution via quadratic forms, and the solution via matrix equations.

Biswa Nath Datta | B. Datta

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