Efficient incremental algorithms for the sparse resultant and the mixed volume

Efficient incremental algorithms for the sparse resultant and the mixed volume (1995)

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by Ioannis Z. Emiris , John F. Canny

Venue:	J. Symbolic Computation
Citations:	39 - 5 self

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Datum	Value	Source
TITLE	Efficient incremental algorithms for the sparse resultant and the mixed volume	user correction
AUTHOR NAME	Ioannis Z. Emiris	user correction
AUTHOR AFFIL	Projet SAFIR, I.N.R.I.A.	user correction
AUTHOR ADDR	B.P. 93, 06902 Sophia-Antipolis, France	user correction
AUTHOR NAME	John F. Canny	user correction
AUTHOR AFFIL	Computer Science Division, University of California	user correction
AUTHOR ADDR	Berkeley CA 94720, USA	user correction
ABSTRACT	We propose a new and efficient algorithm for computing the sparse resultant of a system of n + 1 polynomial equations in n unknowns. This algorithm produces a matrix whose entries are coefficients of the given polynomials and is typically smaller than the matrices obtained by previous approaches. The matrix determinant is a nontrivial multiple of the sparse resultant from which the sparse resultant itself can be recovered. The algorithm is incremental in the sense that successively larger matrices are constructed until one is found with the above properties. For multigraded systems, the new algorithm produces optimal matrices, i.e., expresses the sparse resultant as a single determinant. An implementation of the algorithm is described and experimental results are presented. In addition, we propose an efficient algorithm for computing the mixed volume of n polynomials in n variables. This computation provides an upper bound on the number of common isolated roots. A publicly available implementation of the algorithm is presented and empirical results are reported which suggest that it is the fastest mixed volume code to date.	user correction
YEAR	1995	INFERENCE
VENUE	J. Symbolic Computation	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	14--9	INFERENCE
VOLUME	20	INFERENCE
CITATIONS	69 found	ParsCit 1.0