Abstract In this paper, we present new approaches computing the rank and the null space of the (m
n + p)×(n + p) generalized Sylvester matrix of (m + 1) polynomials of maximal degrees n,p. We introduce an algorithm which handles directly a modification of the generalized Sylvester matrix, computing efficiently
its rank and null space and replacing n by log
2
n in the required complexity of the classical methods. We propose also a modification of the Gauss-Jordan factorization method
applied to the appropriately modified Sylvester matrix of two polynomials for computing simultaneously its rank and null space.
The methods can work numerically and symbolically as well and are compared in respect of their error analysis, complexity
and efficiency. Applications where the computation of the null space of the generalized Sylvester matrix is required, are
also given.
n + p)×(n + p) generalized Sylvester matrix of (m + 1) polynomials of maximal degrees n,p. We introduce an algorithm which handles directly a modification of the generalized Sylvester matrix, computing efficiently
its rank and null space and replacing n by log
2
n in the required complexity of the classical methods. We propose also a modification of the Gauss-Jordan factorization method
applied to the appropriately modified Sylvester matrix of two polynomials for computing simultaneously its rank and null space.
The methods can work numerically and symbolically as well and are compared in respect of their error analysis, complexity
and efficiency. Applications where the computation of the null space of the generalized Sylvester matrix is required, are
also given.
- Content Type Journal Article
- Category Original Paper
- DOI 10.1007/s11075-009-9336-6
- Authors
- Dimitrios Triantafyllou, University of Athens Department of Mathematics Panepistemiopolis 15784 Athens Greece
- Marilena Mitrouli, University of Athens Department of Mathematics Panepistemiopolis 15784 Athens Greece
- Journal Numerical Algorithms
- Online ISSN 1572-9265
- Print ISSN 1017-1398
