Asymptotic acceleration of solving multivariate polynomial systems of equations
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The complexity of the matrix eigenproblem
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximate polynomial Gcds, Padé approximation, polynomial zeros and bipartite graphs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Towards factoring bivariate approximate polynomials
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Polynomial root finding using iterated Eigenvalue computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Univariate polynomials: nearly optimal algorithms for factorization and rootfinding
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
An iterated eigenvalue algorithm for approximating roots of univariate polynomials
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Relations between roots and coefficients, interpolation and application to system solving
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Univariate polynomials: nearly optimal algorithms for numerical factorization and root-finding
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Real computations with fake numbers
Journal of Complexity
Factoring multivariate polynomials via partial differential equations
Mathematics of Computation
On zeros of polynomial and vector solutions of associated polynomial system from Vieta theorem
Applied Numerical Mathematics
A method computing multiple roots of inexact polynomials
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Computer algebra handbook
On solvents of matrix polynomials
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Polynomiography and applications in art, education, and science
ACM SIGGRAPH 2003 Educators Program
Algorithm 835: MultRoot---a Matlab package for computing polynomial roots and multiplicities
ACM Transactions on Mathematical Software (TOMS)
Numerical factorization of multivariate complex polynomials
Theoretical Computer Science - Algebraic and numerical algorithm
A property of the nearly optimal root-bound
Journal of Computational and Applied Mathematics
Improved algorithms for computing determinants and resultants
Journal of Complexity - Special issue: Foundations of computational mathematics 2002 workshops
Computing real roots of a polynomial in Chebyshev series form through subdivision
Applied Numerical Mathematics
On general convergence in extracting radicals via a fundamental family of iteration functions
Journal of Computational and Applied Mathematics
Univariate polynomial real root isolation: continued fractions revisited
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Computing monodromy groups defined by plane algebraic curves
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Null space and eigenspace computations with additive preprocessing
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Stability of IMEX Runge-Kutta methods for delay differential equations
Journal of Computational and Applied Mathematics
On the complexity of real root isolation using continued fractions
Theoretical Computer Science
A two-steps algorithm for approximating real roots of a polynomial in Bernstein basis
Mathematics and Computers in Simulation
Additive preconditioning and aggregation in matrix computations
Computers & Mathematics with Applications
Newton's method and the Computational Complexity of the Fundamental Theorem of Algebra
Electronic Notes in Theoretical Computer Science (ENTCS)
Theoretical Computer Science
Real algebraic numbers and polynomial systems of small degree
Theoretical Computer Science
Schur aggregation for linear systems and determinants
Theoretical Computer Science
Dynamic ham-sandwich cuts in the plane
Computational Geometry: Theory and Applications
Enclosing all zeros of an analytic function - A rigorous approach
Journal of Computational and Applied Mathematics
Isolating real roots of real polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Continued fraction expansion of real roots of polynomial systems
Proceedings of the 2009 conference on Symbolic numeric computation
Accurate semisymbolic analysis of circuits with multiple roots
ICC'09 Proceedings of the 13th WSEAS international conference on Circuits
The amended DSeSC power method for polynomial root-finding
Computers & Mathematics with Applications
Coefficient-free adaptations of polynomial root-finders
Computers & Mathematics with Applications
Method for finding multiple roots of polynomials
Computers & Mathematics with Applications
A deterministic algorithm for isolating real roots of a real polynomial
Journal of Symbolic Computation
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Applications of FFT and structured matrices
Algorithms and theory of computation handbook
New progress in real and complex polynomial root-finding
Computers & Mathematics with Applications
Theoretical Computer Science
Theoretical Computer Science
Efficient real root approximation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
A simple but exact and efficient algorithm for complex root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Root-finding by expansion with independent constraints
Computers & Mathematics with Applications
SqFreeEVAL: An (almost) optimal real-root isolation algorithm
Journal of Symbolic Computation
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Efficient polynomial root-refiners: A survey and new record efficiency estimates
Computers & Mathematics with Applications
Derandomization of dimensionality reduction and SDP based algorithms
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
A descartes algorithm for polynomials with bit-stream coefficients
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
A fitting algorithm for real coefficient polynomial rooting
Journal of Computational and Applied Mathematics
A geometric algorithm for winding number computation with complexity analysis
Journal of Complexity
The computation of multiple roots of a polynomial
Journal of Computational and Applied Mathematics
Empirical study of an evaluation-based subdivision algorithm for complex root isolation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Root finding with threshold circuits
Theoretical Computer Science
Root-refining for a polynomial equation
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
A root isolation algorithm for sparse univariate polynomials
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
On the complexity of solving a bivariate polynomial system
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
When Newton meets Descartes: a simple and fast algorithm to isolate the real roots of a polynomial
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Near optimal tree size bounds on a simple real root isolation algorithm
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Improved bounds for the CF algorithm
Theoretical Computer Science
Theoretical Computer Science
Rational univariate representations of bivariate systems and applications
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
On the infinite families of zero bounds of complex polynomials
Journal of Computational and Applied Mathematics
Finding the number of roots of a polynomial in a plane region using the winding number
Computers & Mathematics with Applications
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The classical problem of solving an nth degree polynomial equation has substantially influenced the development of mathematics throughout the centuries and still has several important applications to the theory and practice of present-day computing. We briefly recall the history of the algorithmic approach to this problem and then review some successful solution algorithms. We end by outlining some algorithms of 1995 that solve this problem at a surprisingly low computational cost.