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TitleSolution of a polynomial system of equations via the eigenvector computation
Author(s) Didier Bondyfalat, Bernard Mourrain, Victor Y. Pan
TextD. Bondyfalat, B. Mourrain, and V. Y. Pan, Solution of a polynomial system of equations via the eigenvector computation, Lin. Alg. and its Appl., 319 (2000), pp. 193-209.
TypeTechnical Report, Misc
AbstractWe propose new techniques and algorithms for the solution of a polynomial system of equations by matrix methods. For such a system, we seek its specified root, at which a fixed polynomial takes its maximum or minimum absolute value on the set of roots. We unify several known approaches and simplify the solution substantially, in particular in the case of an overconstrained polynomial system having only a simple root or a few roots. We reduce the solution to the computation of the eigenvector of an associated dense matrix, but we dene this matrix implicitly, as a Schur complement in a sparse and structured matrix, and then modify the known methods for sparse
eigenvector computation. This enables the acceleration of the solution by roughly factor D, the number of roots. Our experiments show that the computations can be performed numerically, with no
increase of the computational precision, and the iteration converges to the specified root quite fast.
JournalLinear Algebra and its Applications
Pages193 - 209
Translation No
Refereed No