Neville elimination for rank-structured matrices

In this paper it is shown that Neville elimination is suited to exploit the rank structure of an order-r quasiseparable matrix A∈Cn×n by providing a condensed decomposition of A as product of unit bidiagonal matrices, all together specified by O(nr) parameters, at the cost of O(nr3) flops. An application of this result for eigenvalue computation of totally positive rank-structured matrices is also presented.