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Abstract: The problem of evaluating the sign of the determinant of a small matrix arises in many geometric algorithms. Given an n \Theta n matrix A with integer entries, whose columns are all smaller than M in Euclidean norm, the algorithm given here evaluates the sign of the determinant det A exactly. The algorithm requires an arithmetic precision of less than 1:5n + 2 lg M bits. The number of arithmetic operations needed is O(n 3 ) + O(n 2 ) log OD(A)=fi, where OD(A)j det Aj is the product of the... (Update)
Context of citations to this paper: More
...inputs, and iterative algorithms. Many more authors have focused on the problem of the sign of the determinant of a small matrix [14, 9, 21, 39, 5]. Little of that recent work applies to computing determinants of large matrices. Some of these approaches also limit the input...
.... [17, 18] lazy arithmetic [2] tuned computations [17, 18] precision driven computation [46] minimized intermediate computation [8, 5], fast hardware computation [42] and modular arithmetic [17, 5] Libraries supporting basic exact computation have been developed, with...
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BibTeX entry: (Update)
K.L. Clarkson, "Safe and Effective Determinant Evaluation", Proc. 33rd IEEE Symp. on Foundations of Computer Science, pp. 387--395, 1992. http://citeseer.ist.psu.edu/clarkson95safe.html More
@inproceedings{ clarkson92safe,
author = "K. L. Clarkson",
title = "Safe and effective determinant evaluation",
booktitle = "Proc. 31st {IEEE} Symposium on Foundations of Computer Science",
month = "October",
address = "Pittsburgh, PA",
pages = "387-395",
year = "1992",
url = "citeseer.ist.psu.edu/clarkson95safe.html" }
Citations (may not include all citations):717 Theory of Linear and Integer Programming (context) - Schrijver - 1986
227 Factoring polynomials with rational coefficients (context) - Lenstra, Lenstra et al. - 1982
171 Baltimore and London (context) - Golub, Van Loan et al. - 1989
67 Verifiable Implementations of Geometric Algorithms using Fin.. (context) - Milenkovic - 1988
67 Verifiable implementations of geometric algorithms using fin.. (context) - Milenkovic - 1988
59 Epsilon geometry: building robust algorithms from imprecise .. (context) - Salesin, Stolfi et al. - 1989
56 Finite-resolution computational geometry (context) - Greene, Yao - 1986
46 Efficient delaunay triangulation using rational arithmetic (context) - Karasick, Lieber et al. - 1990
36 Double precision geometry: a general technique for calculati.. - Milenkovic - 1989
36 Stable maintenance of point-set triangulations in two dimens.. (context) - Fortune - 1989
33 An algorithmic theory of numbers (context) - Lov'asz - 1986
31 Robust set operations on polyhedral solids (context) - Hoffmann, Hopcroft et al. - 1989
27 Constructing strongly convex hulls using exact or rounded ar.. - Li, Milenkovic - 1990
18 A more efficient algorithm for lattice basis reduction (context) - Schnorr - 1988
10 Geometric algorithms in finite-precision arithmetic (context) - Sugihara, Iri - 1988
9 personal communication (context) - Fortune
6 Iterative algorithms for Gram-Schmidt orthogonalization (context) - Hoffman - 1989
The graph only includes citing articles where the year of publication is known.
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More Output-Sensitive Geometric Algorithms (Extended Abstract) - Clarkson (Correct)
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