Fast Stable Solvers for Sequentially Semi-Seperable Linear Systems of Equations
S. Chandrasekaran, P. Dewilde, Ming Gu, T. Pals, Anne van der Veen, Dougľas R. White · 2003
We define the class of sequentially semi-separable matrices in this paper. Essentially this is the class of matrices which have low numerical rank on their off diagonal blocks. Examples include banded matrices, semi-separable matrices, their sums as well as inverses of these sums. Fast and stable algorithms for solving linear systems of equations involving such matrices and computing Moore-Penrose inverses are presented. Supporting numerical results are also presented. In addition, fast algorithms to construct and update this matrix structure for any given matrix are presented. Finally, numerical results that show that the coefficient matrices resulting from global spectral discretizations of certain integral equations indeed have this matrix structure are given.