On a block implementation of Hessenberg multishift QR iteration
International Journal of High Speed Computing
LAPACK's user's guide
A stochastic arithmetic for reliable scientific computation
Mathematics and Computers in Simulation
Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
Numerische Mathematik
Solving algebraic systems using matrix computations
ACM SIGSAM Bulletin
Matrix eigenproblems are at the heart of polynomial system solving
ACM SIGSAM Bulletin
Gröbner bases and matrix eigenproblems
ACM SIGSAM Bulletin
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Matrix algorithms
Multivariate polynomial system solving using intersections of Eigenspaces
Journal of Symbolic Computation
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Generalized normal forms and polynomial system solving
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Selecting lengths of floats for the computation of approximate Gröbner bases
Journal of Symbolic Computation
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This paper provides a new method for computing numerical approximations of the roots of a zero-dimensional system. It works on general systems, even those with multiple roots, and avoids any arbitrary choice of linear combination of the multiplication operators. It works by computing eigenvectors (or a basis of the full invariant subspaces). The sparsity/structure of the multiplication operators by one variable can also be taken into account.