Accurate Computations with Generalized Pascal k-Eliminated Functional Matrices - Jorge Delgado; Héctor Orera; Juan Manuel Peña (Mathematics)
This paper presents an accurate method to obtain the bidiagonal decomposition of some generalized Pascal matrices, including Pascal k-eliminated functional matrices and Pascal symmetric functional matrices. Sufficient conditions to assure that these matrices are either totally positive or inverse of totally positive matrices are provided. In these cases, the presented method can be used to compute their eigenvalues, singular values and inverses with high relative accuracy. Numerical examples illustrate the high accuracy of our approach.