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MIXED BLOCK ELIMINATION FOR LINEAR-SYSTEMS WITH WIDER BORDERS.

The paper is about the stable solution of possibly ill-conditioned bordered linear systems. Given stable solvers for matrix A and for A T , we prove that the Govaerts Mixed Block Elimination (BEM) method constitutes a stable solver for the matrix consisting of A or A T 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