Details:
Title  Solution of a polynomial system of equations via the eigenvector computation  Author(s)  Didier Bondyfalat, Bernard Mourrain, Victor Y. Pan  Text  D. 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. 193209.  Type  Technical Report, Misc  Abstract  We 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. 
Language  English  Journal  Linear Algebra and its Applications  Pages  193  209  Year  2000  Edition  0  Translation 
No  Refereed 
No 
