Mixed block elimination for linear systems with wider borders
Willy J. F. Govaerts, J. D. PRYCE · IMA Journal of Numerical Analysis · 1993
The paper is about the stable solution of possibly ill-conditioned bordered linear systems. Given stable solvers for matrix A and for AT, we prove that the Govaerts Mixed Block Elimination (BEM) method constitutes a stable solver for the matrix consisting of A or AT with a border of width 1, and hence by recursion for a border of any width. We express the algorithm in an efficient, iterative, form. We analyse its operation count, and verify the theory by extensive numerical experiments.