A stopping criterion for polynomial root finding
Communications of the ACM
Corrections to numerical data on Q-D algorithm
Communications of the ACM
Finding zeros of a polynomial by the Q-D algorithm
Communications of the ACM
ACM Transactions on Mathematical Software (TOMS)
Principles for Testing Polynomial Zerofinding Programs
ACM Transactions on Mathematical Software (TOMS)
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Polynomial root finding using iterated Eigenvalue computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Approximate multivariate polynomial factorization based on zero-sum relations
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
A formula for separating small roots of a polynomial
ACM SIGSAM Bulletin
An iterated eigenvalue algorithm for approximating roots of univariate polynomials
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
The reliable algorithmic software challenge RASC
Computer Science in Perspective
Enclosing clusters of zeros of polynomials
Journal of Computational and Applied Mathematics
Ten methods to bound multiple roots of polynomials
Journal of Computational and Applied Mathematics
Computing monodromy groups defined by plane algebraic curves
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Structured matrix methods for polynomial root-finding
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Computing clustered close-roots of univariate polynomials
Proceedings of the 2009 conference on Symbolic numeric computation
A descartes algorithm for polynomials with bit-stream coefficients
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Nonexistence results for tight block designs
Journal of Algebraic Combinatorics: An International Journal
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Given N approximations to the zeros of an Nth-degree polynomial, N circular regions in the complex z-plane are determined whose union contains all the zeros, and each connected component of this union consisting of K such circular regions contains exactly K zeros. The bounds for the zeros provided by these circular regions are not excessively pessimistic; that is, whenever the approximations are sufficiently well separated and sufficiently close to the zeros of this polynomial, the radii of these circular regions are shown to overestimate the errors by at most a modest factor simply related to the configuration of the approximations. A few numerical examples are included.