Exact primitives for smallest enclosing ellipses

Information Processing Letters

Volumn 68, Issue 1, 1998, Pages 33-38

  Gärtner, Bernd ^a   Schönherr, Sven ^b  

^a ETH ZURICH   (Switzerland)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Computational complexity; Computational geometry; L wner John ellipsoid; Primitive operations

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; MATHEMATICAL PROGRAMMING; NUMERICAL METHODS; POLYNOMIALS; SET THEORY;

CONVEX PROGRAMMING; LOWNER-JOHN ELLIPSOID; PRIMITIVE OPERATIONS; WELZL ALGORITHMS; WELZL RANDOMIZED METHOD;

ALGORITHMS;

EID: 0032178808     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-0190(98)00132-x     Document Type: Article

References (18)

1. I. Adler, R. Shamir, A randomization scheme for speeding up algorithms for linear and convex quadratic programming problems with a high constraints-to-variables ratio, Math. Programming 61 (1993) 39-52.
2. L. Danzer, D. Laugwitz, H. Lenz, Über das Löwnersche Ellipsoid und sein Analogon unter den einem Eikörper eingeschriebenen Ellipsoiden, Arch. Math. 8 (1957) 214-219.
3. M.E. Dyer, A class of convex programs with applications to computational geometry, in: Proc. 8th Annual ACM Symp. on Computational Geometry, 1992, pp. 9-15.
4. B. Gärtner, S. Schönherr, Exact primitives for smallest enclosing ellipses, in: Proc. 13th Annual ACM Symp. on Computational Geometry, 1997, pp. 430-432.
5. B. Gärtner, E. Welzl, Linear programming - randomization and abstract frameworks, in: Proc. 13th Annual Symp. on Theoretical Aspects of Computer Science (STAGS), Lecture Notes in Computer Sci., Vol. 1046, Springer, Berlin, 1996, pp. 669-687.
6. F. John, Extremum problems with inequalities as subsidiary conditions, in: Studies and Essays presented to R. Courant on his 60th Birthday, Interscience Publishers, New York, 1948, pp. 187-204.
7. J. Matoušek, M. Sharir, E. Welzl, A subexponential bound for linear programming, in: Proc. 8th Annual ACM Symp. Computational Geometry, 1992, pp. 1-8.
8. K. Mehlhorn, S. Näher, LEDA: a platform for combinatorial and geometric computing, Comm. ACM 38 (1995) 96-102.
9. M.J. Post, Computing minimum spanning ellipses, Technical Report CS-82-16, Department of Computer Science, Brown University, 1982.
10. M.J. Post, Minimum spanning ellipsoids, in: Proc. 16th Annual ACM Symp. Theory of Computing, 1984, pp. 108-116.
11. L. Pronzato, E. Walter, Minimum-volume ellipsoids containing compact sets: Applications to parameter bounding, Automatica 30 (11) (1994) 1731-1739.
12. S. Schönherr, Berechnung kleinster Ellipsoide um Punktemengen, Diploma thesis, Free University Berlin, 1994.
13. N.Z. Shor, O.A. Berezovski, New algorithms for constructing optimal circumscribed and inscribed ellipsoids, Opt. Methods Software 1 (1992) 283-299.
14. B.W. Silverman, D.M. Titterington, Minimum covering ellipses, SIAM J. Sci. Statist. Comput. 1 (1980) 401-409.
15. B. Spain, Analytical Conics, Pergamon Press, 1957.
16. D.M. Titterington, Optimal design: some geometrical aspects of D-optimality, Biometrika 62 (2) (1975) 313-320.
17. D.M. Titterington, Estimation of correlation coefficients by ellipsoidal trimming, Appl. Statist. 27 (3) (1978) 227-234.
18. E. Welzl, Smallest enclosing disks (balls and ellipsoids), in: H. Maurer (Ed.), New Results and New Trends in Computer Science, Lecture Notes in Computer Sci., Vol. 555, Springer, Berlin, 1991, pp. 359-370.