On constructing orthogonal generalized doubly stochastic matrices
For researchers in matrix theory and numerical linear algebra, the paper provides constructive methods for a specialized class of matrices, but the contribution is incremental.
The paper proposes numerically stable methods for generating orthogonal generalized doubly stochastic matrices and solves an inverse eigenvalue problem for such matrices with prescribed eigenvalues. MATLAB tests demonstrate the algorithms' numerical stability.
A real quadratic matrix is generalized doubly stochastic (g.d.s.) if all of its row sums and column sums equal one. We propose numerically stable methods for generating such matrices having possibly orthogonality property or/and satisfying Yang-Baxter equation (YBE). Additionally, an inverse eigenvalue problem for finding orthogonal generalized doubly stochastic matrices with prescribed eigenvalues is solved here. The tests performed in \textsl{MATLAB} illustrate our proposed algorithms and demonstrate their useful numerical properties.