Approximate GCD and its application to ill-conditioned algebraic equations
ISCM '90 Proceedings of the International Symposium on Computation mathematics
Journal of Computational and Applied Mathematics
Optimization strategies for the approximate GCD problem
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On approximate GCDs of univariate polynomials
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
Computation of approximate polynomial GCDs and an extension
Information and Computation
The Thirteen Books of Euclid's Elements, Books 1 and 2
The Thirteen Books of Euclid's Elements, Books 1 and 2
Structured matrix-based methods for polynomial ∈-gcd: analysis and comparisons
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
The ERES method for computing the approximate GCD of several polynomials
Applied Numerical Mathematics
Numerical Linear Algebra and Applications, Second Edition
Numerical Linear Algebra and Applications, Second Edition
The calculation of the degree of an approximate greatest common divisor of two polynomials
Journal of Computational and Applied Mathematics
QR factoring to compute the GCD of univariate approximate polynomials
IEEE Transactions on Signal Processing
Hi-index | 7.29 |
The Extended-Row-Equivalence and Shifting (ERES) method is a matrix-based method developed for the computation of the greatest common divisor (GCD) of sets of many polynomials. In this paper we present the formulation of the shifting operation as a matrix product which allows us to study the fundamental theoretical and numerical properties of the ERES method by introducing its complete algebraic representation. Then, we analyse in depth its overall numerical stability in finite precision arithmetic. Numerical examples and comparison with other methods are also presented.