T. Mulders and A. Storjohann, On lattice reduction for polynomial matrices, J. Symb. Comp., 35(4):377--401, 2003. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
On the Complexity of Polynomial Matrix Computations - Giorgi, Jeannerod (2003) (Correct)
....d j denote the degree of the jth column of C. The corresponding coe#cient vector of x d j is the jth leading vector of C. We let [C] l be the matrix of these leading vectors. Definition 3.1 A matrix C is column reduced if its leading coe#cient matrix satisfies rank [C] l = rank C. We refer to [14, 22] and the references therein for discussions on previous reduction algorithms and applications of the form especially in linear algebra and in linear control theory. If r is the rank of A, the best previously known cost for reducing A was O(n rd ) operations in K [14] Thus in particular ....
....rank C. We refer to [14, 22] and the references therein for discussions on previous reduction algorithms and applications of the form especially in linear algebra and in linear control theory. If r is the rank of A, the best previously known cost for reducing A was O(n rd ) operations in K [14]. Thus in particular O(n ) for a nonsingular matrix. Here we propose a di#erent approach which takes advantage of fast polynomial matrix multiplication and gives in particular the complexity estimate O(n d) We assume that A of degree d is nonsingular in K[x] The general case would ....
T. Mulders and A. Storjohann. On lattice reduction for polynomial matrices. Journal of Symbolic Computation. To appear.
Normal Forms for General Polynomial Matrices - Beckermann, Labahn (2002) (1 citation) (Correct)
....method for computing Hermite or (shifted) Popov forms for general matrix polynomials has not been previously given. Algorithms and complexities to compute the Popov form or column reduced forms over K[z] with K an abstract eld have been studied in [34] see also the references therein) or in [24]. Many algorithms have been proposed to compute the Hermite form over K[z] the reader may refer to [30] for an overview of the domain. For concrete coe cient domains like ZZ , expression swell on the coe cient level leads in general to a severe breakdown of the methods performance. The case of ....
T. Mulders and A. Storjohann, On lattice reduction for polynomial matrices, Tech. Rep. 356, Department of Computer Science, ETH Zurich Switzerland, dec. 2000.
Normal Forms for General Polynomial Matrices - Beckermann, Labahn, Villard (2001) (1 citation) (Correct)
....method for computing Hermite or (shifted) Popov forms for general matrix polynomials has not been previously given. Algorithms and complexities to compute the Popov form or column reduced forms over K[z] with K an abstract eld have been studied in [34] see also the references therein) or in [24]. Many algorithms have been proposed to compute the Hermite form over K[z] the reader may refer to [30] for an overview of the domain. For concrete coecient domains like ZZ , expression swell on the coecient level leads in general to a severe breakdown of the methods performance. The case of ....
T. Mulders and A. Storjohann, On lattice reduction for polynomial matrices, Tech. Rep. 356, Department of Computer Science, ETH Zurich Switzerland, dec. 2000.
On The Complexity Of Computing Determinants (Extended Abstract) - Kaltofen, Villard (Correct)
....polynomial of O(n 2.80652 (# =0.34, # =0.23) 5 Conclusion Our methods apply to entry domains other than the integers, like polynomial rings and algebraic number rings. We would like to add that if the entries are polynomials over a finite field, there are di#erent techniques possible [26]. Our determinant algorithm for integer matrices may be extended to a Monte Carlo method for computing the integral Smith normal form of an integral matrix by the techniques described in [18] The reduction of the bit complexity of an algebraic problem below that of its known algebraic complexity ....
T. Mulders and A. Storjohann. On lattice reduction for polynomial matrices. Manuscript available from http://www.scl.csd.uwo.ca/ ~storjoha/, 2001. 14
On The Complexity Of Computing Determinants (Extended Abstract) - Kaltofen, Villard (Correct)
....polynomial of O(n 2.80652 ) # =0.34, # =0.23) 5Conclusion Our methods apply to entry domains other than the integers, like polynomial rings and algebraic number rings. We would like to add that if the entries are polynomials over a finite field, there are di#erent techniques possible [26]. Our determinant algorithm for integer matrices may be extended to a Monte Carlo method for computing the integral Smith normal form of an integral matrix by the techniques described in [18] The reduction of the bit complexity of an algebraic problem below that of its known algebraic complexity ....
T. Mulders and A. Storjohann. On lattice reduction for polynomial matrices. Manuscript available from http://www.scl.csd.uwo.ca/ 26 ~storjoha/, 2001.
Essentially Optimal Computation of the Inverse of Generic.. - Jeannerod (Correct)
No context found.
T. Mulders and A. Storjohann, On lattice reduction for polynomial matrices, J. Symb. Comp., 35(4):377--401, 2003.
On the Complexity of Polynomial Matrix Computations - Giorgi, Jeannerod, Villard (2003) (Correct)
No context found.
T. Mulders and A. Storjohann. On lattice reduction for polynomial matrices. Journal of Symbolic Computation, 35(4):377--401, 2003.
Normal Forms for General Polynomial Matrices - Bernhard Beckermann George (2001) (1 citation) (Correct)
No context found.
T. Mulders and A. Storjohann, On lattice reduction for polynomial matrices, Journal of Symbolic Computation, 35, (2003) 377-401.
Algorithms for Normal Forms for Matrices of Polynomials and Ore.. - Cheng (2003) (Correct)
No context found.
T. Mulders and A. Storjohann. On lattice reduction for polynomial matrices. Journal of Symbolic Computation, 35(4):377--401, 2003.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC