Root neighborhoods of a polynomial
Mathematics of Computation
An algorithm to compute floating point Gro¨bner bases
Proceedings of the Maple summer workshop and symposium on Mathematical computation with Maple V : ideas and applications: ideas and applications
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Efficient algorithms for computing the nearest polynomial with constrained roots
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
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Remarks on automatic algorithm stabilization
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Efficient algorithms for computing the nearest polynomial with a real root and related problems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Pseudofactors of multivariate polynomials
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
The nearest polynomial with a given zero, and similar problems
ACM SIGSAM Bulletin
A note on a nearest polynomial with a given root
ACM SIGSAM Bulletin
The nearest polynomial with a given zero, revisited
ACM SIGSAM Bulletin
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Locating real multiple zeros of a real interval polynomial
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Interval linear systems: the state of the art
Computational Statistics
On real factors of real interval polynomials
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Determining divisibility between polynomials with inexact coefficients
ACM Communications in Computer Algebra
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For a real multivariate interval polynomial P and a real multivariate polynomial f, we provide a rigorous method for deciding whether there is a polynomial p in P such that f is a factor of p. When P is univariate, there is a well-known criterion for whether there exists a polynomial p in P such that p(a)=0 for a given real number a. Since p(a)=0 if and only if x-a is a factor of p, our result is a generalization of the criterion to multivariate polynomials and higher degree factors. Furthermore, for real multivariate polynomials p and f, we show a method for computing a nearest polynomial q to p in a weighted l^~-norm such that f is a factor of q.