On lattice reduction for polynomial matrices

Journal of Symbolic Computation

Volumn 35, Issue 4, 2003, Pages 377-401

  Mulders, Thom ^a   Storjohann, A ^b  

^a COMIT AG ^*  (Switzerland)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Determinant; Hermite form; Lattice reduction; Polynomial matrices; Popov form; Rank profile

Indexed keywords

EID: 0038405094     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0747-7171(02)00139-6     Document Type: Article

References (16)

1. Atiyah, M.F., MacDonald, I.G., 1969. Introduction to Commutative Algebra, Addison-Wesley, New York.
2. Beckermann, B., Labahn, G., Villard, G., 1999. Shifted normal forms of polynomial matrices. In: Dooley, S. (Ed.), Proceedings of the Int'l. Symp. on Symbolic and Algebraic Computation: ISSAC '99, ACM Press, New York, pp. 189-196.
3. Beckermann, B., Labahn, G., Villard, G., 2002. Normal forms for general polynomial matrices, Research Report 2002-1, ENS Lyon, France.
4. Domich, P.D., Kannan, R., Trotter, L.E. Jr., 1987. Hermite normal form computation using modulo determinant arithmetic. Mathematics of Operations Research 12 (1), 50-59.
5. von zur Gathen, J., 1984. Hensel and Newton methods in valuation rings. Mathematics of Computation 42, 637-661.
6. von zur Gathen, J., Gerhard, J., 1999. Modern Computer Algebra, Cambridge University Press, Cambridge.
7. Kailath, T., 1980. Linear Systems, Prentice-Hall, New Jersey.
8. Labhalla, S., Lombardi, H., Marlin, R., 1996. Algorithmes de calcul de la réduction de Hermite d'une matrice à coefficients polynomiaux. Theoretical Computer Science 161, 69-92.
9. MacDuffee, C.C., 1956. The Theory of Matrices, Chelsea, New York.
10. Mulders, T., Storjohann, A., 2000a. Certified dense linear system solving. Techreport 355, ETH Zurich, Department of Computer Science. Journal of Symbolic Computation (to appear).
11. Mulders, T., Storjohann, A., 2000b. Rational solutions of singular linear systems. In: Traverso, C. (Ed.), Proceedings of the Int'l. Symp. on Symbolic and Algebraic Computation: ISSAC'00, ACM Press, New York, pp. 242-249.
12. Newman, M., 1972. Integral Matrices, Academic Press, New York.
13. Popov, V., 1969. Some properties of control systems with irreducible matrix transfer functions. In: Lecture Notes in Mathematics, vol. 144, Springer, New York.
14. Storjohann, A., 2002. High-order lifting. In: Mora, T. (Ed.), Proceedings of the Int'l. Symp. on Symbolic and Algebraic Computation: ISSAC'02, ACM Press, New York, pp. 246-254.
15. Villard, G., 1996. Computing Popov and Hermite forms of polynomial matrices. In: Lakshman, Y.N. (Ed.), Proceedings of the Int'l. Symp. on Symbolic and Algebraic Computation: ISSAC'96, ACM Press, New York, pp. 250-258.
16. # compiler. In: Giesbrecht, (Ed.), Proceedings of the Int'l. Symp. on Symbolic and Algebraic Computation: ISSAC '94, ACM Press, New York, pp. 25-31.