On the infinitesimal limits of the Schur complements of tridiagonal matrices

Abstract: In this paper we consider diagonally dominant tridiagonal matrices whose diagonals come from smooth functions. It is shown that the Schur complements or pivots that arise from Gaussian elimination of these matrices can be given point-wise limits on a grid as the matrices grow in size to infinity. Numerical results are presented to verify the theory. [Copyright &y& Elsevier]