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On the Bit Complexity of Solving Bilinear Polynomial Systems

2016
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Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16
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We bound the Boolean complexity of computing isolating hyperboxes for all complex roots of systems of bilinear polynomials. The resultant of such systems admits a family of determinantal Sylvester-type formulas, which we make explicit by means of homological complexes. The computation of the determinant of the resultant matrix is a bottleneck for the overall complexity. We exploit the quasi-Toeplitz structure to reduce the problem to efficient matrix-vector products, corresponding to

doi:10.1145/2930889.2930919
dblp:conf/issac/EmirisMT16
fatcat:ou73donorbhvfbwes7dzlrxaoy