A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots

The technique of solving systems of multivariate polynomial equations via rigenproblems has become a topic of active research (with applications in computer-aided design and {untrul theory, for example) at least since the papers [2, 6, 9]. one may approach the problem via various resultant formulations ,x by Grijbner bases. As more understanding is gained, it is becoming clearer that eigenvalue problems are the “weakly nonlinear nucleus to which the original, strongly nonlinear task may be reduced’ [13], Earl,v works mmcemt,rat,ed on the case of simple roots. An example of such was, the paper [5], which used a numerical adaptation of il resultant technique due to Lazard to attack the problem directly, without, reference to Grobner bases.