Details:
Title  Symmetric subresultants and applications  Author(s)  Cyril Brunie, Philippe Saux Picart  Type  Article in Journal  Abstract  Schur’s transforms of a polynomial are used to count its roots in the unit disk. These are generalized then by introducing the sequence of symmetric subresultants of two polynomials. Although they do have a determinantal definition, we show that they satisfy a structure theorem which allows us to compute them with a type of Euclidean division. As a consequence, a fast algorithm based on a dichotomic process and FFT is designed. We prove also that these symmetric subresultants have a deep link with Toeplitz matrices. Finally, we propose a new algorithm of inversion for such matrices. It has the same cost as those already known; however it is fraction free and consequently well adapted to computer algebra.  Keywords  Subresultant, Toeplitz matrices, Matrix inversion, DFT, Fractionfree algorithm, Euclidean division  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717107000740 
Language  English  Journal  Journal of Symbolic Computation  Volume  42  Number  9  Pages  884  919  Year  2007  Edition  0  Translation 
No  Refereed 
No 
