A HYBRID APPROACH FOR DETERMINANT SIGNS OF MODERATE-SIZED MATRICES
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Many geometric computations have at their core the evaluation of the sign of the determinant of a matrix. A fast, failsafe determinant sign operation is often a key part of a robust implementation. While linear problems from 3D computational geometry usually require determinants no larger than six, non-linear problems involving algebraic curves and surfaces produce larger matrices. Furthermore, the matrix entries often exceed machine precision, while existing approaches focus on machine-precision matrices. In this paper, we describe a practical hybrid method for computing the sign of the determinant of matrices of order up to 60. The stages include a floating-point filter based on the singular value decomposition of a matrix, an adaptive-precision implementation of Gaussian elimination, and a standard modular arithmetic determinant algorithm. We demonstrate our method on a number of examples encountered while solving polynomial systems.
author list (cited authors)
CULVER, T., KEYSER, J., MANOCHA, D., & KRISHNAN, S.