On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
SIAM Journal on Numerical Analysis
Fundamentals of matrix computations
Fundamentals of matrix computations
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Common factor detection and estimation
Automatica (Journal of IFAC)
Polynomials and Linear Control Systems
Polynomials and Linear Control Systems
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A composite algorithm for finding zeros of real polynomials
A composite algorithm for finding zeros of real polynomials
Approximate factorization of multivariate polynomials via differential equations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
High Order Terms for Condition Estimation of Univariate Polynomials
SIAM Journal on Scientific Computing
Structured matrix-based methods for polynomial ∈-gcd: analysis and comparisons
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Structured total least norm and approximate GCDs of inexact polynomials
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
The MDL criterion for rank determination via effective singularvalues
IEEE Transactions on Signal Processing
QR factoring to compute the GCD of univariate approximate polynomials
IEEE Transactions on Signal Processing
Blind image deconvolution using a robust GCD approach
IEEE Transactions on Image Processing
The computation of multiple roots of a polynomial
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
The calculation of the degree of an approximate greatest common divisor (AGCD) of two inexact polynomials f(y) and g(y) is a non-trivial computation because it reduces to the estimation of the rank loss of a resultant matrix R(f,g). This computation is usually performed by placing a threshold on the small singular values of R(f,g), but this method suffers from disadvantages because the numerical rank of R(f,g) may not be defined, or the noise level imposed on the coefficients of f(y) and g(y) may not be known, or it may only be known approximately. This paper addresses this problem by considering two methods for estimating the degree of an AGCD of f(y) and g(y), such that knowledge of the noise level is not required. The first method involves the calculation of the smallest angle between two subspaces that are apparent from the structure of the Sylvester resultant matrix S(f,g), and the second method uses the theory of subresultant matrices, which are derived from S(f,g) by the deletion of some of its rows and columns. The two methods are compared computationally on non-trivial polynomials.