Bounds for absolute positiveness of multivariate polynomials

Journal of Symbolic Computation

Volumn 25, Issue 5, 1998, Pages 571-585

  Hong, Hoon ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032066673     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1997.0189     Document Type: Article

References (40)

1. Akritas, A., Collins, G. E. (1976). Polynomial real root isolation using Descartes' rule of signs. In Proceedings of SYMSAC 76, pp. 272-275. New York: ACM.
2. Arnon, D. S. (1981). Algorithms for the Geometry of Semi-Algebraic Sets. PhD thesis, Comp. Sci. Dept., Univ. of Wisconsin-Madison. Tech. Report No. 436.
3. Ben-Cherifa, A., Lescanne, P. (1987). Termination of rewriting systems by polynomial interpretations and its implementation. Sci. Comput. Program. 9, 137-159.
4. Berwald, L. (1934). Elementare Sätze über die Abgrenzung der Wurzeln einer algebraischen Gleichung. Acta Sci. Math. Litt. Sci. Szeged 6, 209-221.
5. Birkhoff, G. D. (1914). An elementary double inequality for the roots of an algebraic equation having greatest absolute value. Bull. Am. Math. Soc. 21, 494-495.
6. Borwein, P., Erdelyi, T. (1995). Polynomials and Polynomial Inequalities. Berlin: Springer Verlag.
7. Canny, J. (1988). Some algebraic and geometric computations in PSPACE. In Proceedings of the 20th annual ACM symposium on the theory of computing, pp. 460-467.
8. Carmichael, R. D., Mason, T. E. (1914). Note on the roots of an algebraic equations. Bull. Am. Math. Soc. 21, 14-22.
9. Cauchy, A. L. (1829). Exercises de mathematique. Oeuvres 9, 122.
10. Cohn, A. (1922). Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise. Math. Z. 14, 110-148.
11. Collins, G. E. (1975). Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. In Lecture Notes In Computer Science, 33, pp. 134-183. Berlin: Springer-Verlag.
12. Collins, G. E., Hong, H. (1991). Partial cylindrical algebraic decomposition for quantifier elimination. J. Symb. Comput. 12, 299-328.
13. Collins, G. E., Johnson, J. R., Kuechlin, W. (1992). Parallel real root isolation using the coefficient sign variation method. In Zippel, R. E., ed., Proc. Computer Algebra and Parallelism, pp. 71-88. Berlin: Springer-Verlag.
14. Collins, G. E., Krandick, W. (1992). An efficient algorithm for infallible polynomial complex root isolation. In Wang, P. S., ed, ISSAC-92, pp. 189-194. New York: ACM.
15. Collins, G. E., Krandick, W. (1993). A hybrid method for high precision calculation of polynomial real roots. In Bronstein, M., ed., ISSAC-93, pp. 47-52. New York: ACM.
16. Collins, G. E., Loos, R. (1976). Polynomial real root isolation by differentiation. In Proceedings of SYMSAC 76, pp. 15-25. New York: ACM.
17. Dershowitz, N. (1987). Termination of rewriting. J. Symb. Comput. 3:69-116.
18. Fujiwara, M. (1915). Über die Wurzeln der algebraischen Gleichungen. Tôhoku Math. J. 8:78-85.
19. Giesl, J. (1995). Generating polynomial orderings for termination proofs. In Proceedings of the 6th International Conference on Rewriting Techniques and Applications Lecture Notes in Computer Science, 914. Kaiserslautern: Springer-Verlag.
20. Grigor'ev, D. Y. (1988). The complexity of deciding Tarski algebra. J. Symb. Comput. 5, 65-108.
21. Heindel, L. E. (1970). Algorithms for Exact Polynomial Root Calculation. PhD thesis, University of Wisconsin.
22. Heintz, J., Roy, M.-F., Solernó, P. (1989). On the complexity of semialgebraic sets. In Ritter, G. X., ed., Proc. IFIP, pp. 293-298. Amsterdam: North-Holland.
23. Hong, H. (1990). Improvements in CAD-based Quantifier Elimination. PhD thesis, The Ohio State University.
24. Hong, H., Jakus, D. (1996). Testing Positiveness of Polynomials. Technical Report 96-02, RISC-Linz, Johannes Kepler University, Linz, Austria.
25. Johnson, J. R. (1991). Algorithms for Polynomial Real Root Isolation. PhD thesis, The Ohio State University.
26. Johnson, J. R. (1992). Real algebraic number computation using interval arithmetic. In Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 195-205. New York: ACM.
27. Kelleher, S. B. (1916). Des limites des zéros dùn polynome. J. Math. Pres Appl. 2, 169-171.
28. Kuniyeda, M. (1916). Note on the roots of algebraic equations. Tôhoku Math. J. 9, 167-173.
29. Lankford, D. (1976). A finite termination algorithm. Technical report, Southwestern University, Georgetown, Texas.
30. Lucas, F. (1874). Propriétés géométriques des fractions rationnelles. C. R. Acad. Sci. Paris 77, 431-433.
31. Marden, M. (1949). The Geometry of Zeros of a Polynomial in a Complex Variable, vol. 3 of Mathematics Surveys. Providence, RI: American Mathematics Society.
32. McCallum, S. (1984). An Improved Projection Operator for Cylindrical Algebraic Decomposition. PhD thesis, University of Wisconsin-Madison.
33. Milovanovic, G., Mitrinovic, D., Rassias, T. (1994). Topics in Polynomials: Extremal Problems, Inequalities, Zeros. Singapore: World Scientific.
34. Montel, P. (1932). Sur La limite supérieure du module des racines dùne équation algébrique. C. R. Soc. Sci. Varsovie 24, 317-326.
35. Renegar, J. (1992). On the computational complexity and geometry of the first-order theory of the reals. J. Symb. Comput. 13, 255-300.
36. Steinbach, J. (1992). Proving Polynomials Positive. In Proc. 12th FST&TCS, LNCS 652, New Delhi, India.
37. Steinbach, J. (1994). Termination of rewriting. PhD thesis. University of Kaiserslautern, Germany.
38. Tarski, A. (1951). A Decision Method for Elementary Algebra and Geometry (2nd edn). Berkeley, CA: University of California Press.
39. Tôya, T. (1933). Some remarks on Montel's paper concerning upper limit of absolute values of roots of algebraic equations. Sci. Rep. Tokyo Bunrika Daigaku A 1:275-282.
40. Weispfenning, V. (1988). The complexity of linear problems in fields. J. Symb. Comput. 5, 3-27.