Solution of elementary equations in the Minkowski geometric algebra of complex sets

Advances in Computational Mathematics

Volumn 22, Issue 4, 2005, Pages 301-323

  Farouki, Rida T ^a   Han, Chang Yong ^a  

^a University of California Davis   (United States)

Author keywords

Cartesian oval; Equations in complex sets; Logarithmic Gauss map; Maximal solution; Minkowski geometric algebra; Ovals of Cassini

Indexed keywords

EID: 17544362257     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-003-2605-3     Document Type: Article

References (16)

1. R.T. Farouki and J.-C.A. Chastang, Curves and surfaces in geometrical optics, in: Mathematical Methods in Computer Aided Geometric Design, Vol. II, eds. T. Lyche and L.L. Schumaker (Academic Press, New York, 1992) pp. 239-260.
2. R.T. Farouki and J.-C.A. Chastang, Exact equations of "simple" wavefronts, Optik 91 (1992) 109-121.
3. R.T. Farouki, W. Gu and H.P. Moon, Minkowski roots of complex sets, in: Geometric Modeling and Processing 2000 (IEEE Computer Soc. Press, Los Alamitos, CA, 2000) pp. 287-300.
4. R.T. Farouki and H.P. Moon, Minkowski geometric algebra and the stability of characteristic polynomials, in: Visualization and Mathematics, Vol. 3, eds. H.-C. Hege and K. Polthier (Springer, Berlin, 2003) pp. 163-188.
5. R.T. Farouki, H.P. Moon and B. Ravani, Algorithms for Minkowski products and implicitly-defined complex sets, Adv. Comput. Math. 13 (2000) 199-229.
6. R.T. Farouki, H.P. Moon and B. Ravani, Minkowski geometric algebra of complex sets, Geometriae Dedicata 85 (2001) 283-315.
7. R.T. Farouki and H. Pottmann, Exact Minkowski products of N complex disks, Reliable Comput. 8 (2002) 43-66.
8. I. Gargantini and P. Henrici, Circular arithmetic and the determination of polynomial zeros, Numer. Math. 18 (1972) 305-320.
9. F. Gomes Teixeira, Traité des Courbes Spéciales Remarquables Planes et Gauches, Tome I (reprint) (Chelsea, New York, 1971).
10. M. Hauenschild, Arithmetiken für komplexe Kreise, Computing 13 (1974) 299-312.
11. M. Hauenschild, Extended circular arithmetic, problems and results, in: Interval Mathematics 1980, ed. K.L.E. Nickel (Academic Press, New York, 1980) pp. 367-376.
12. J.D. Lawrence, A Catalog of Special Plane Curves (Dover, New York, 1972).
13. E.H. Lockwood, A Book of Curves (Cambridge Univ. Press, Cambridge, 1967).
14. R.E. Moore, Interval Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1966).
15. R.E. Moore, Methods and Applications of Interval Analysis (SIAM, Philadelphia, PA, 1979).
16. M.S. Petković and L.D. Petković, Complex Interval Arithmetic and Its Applications (Wiley/VCH, Berlin, 1998).