Bidiagonal decompositions, minors and applications

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A. Barreras
J. Peña


Matrices, called ε-BD matrices, that have a bidiagonal decomposition satisfying some sign constraints are analyzed. The ε-BD matrices include all nonsingular totally positive matrices, as well as their matrices opposite in sign and their inverses. The signs of minors of ε-BD matrices are analyzed. The zero patterns of ε-BD matrices and their triangular factors are studied and applied to prove the backward stability of Gaussian elimination without pivoting for the associated linear systems.

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