A test and bidiagonal factorization for certain sign regular matrices

It is well known that a totally nonnegative matrix can be characterized in terms of its bidiagonal factorization, which is critical to perform accurate computations. However, there is no known such factorization of other sign regular matrices. In this paper, we provide a characterization and test for certain sign regular matrices with the same signature sequence as that of nonsingular Jacobi sign regular matrices. Consequently, a bidiagonal factorization is derived for such sign regular matrix, which, in turn, provides an effective way to generate these sign regular matrices.