EMIRIS , Ioannis

It has by now become a standard approach to use the theory of sparse (or toric) elimination, based on the Newton polytope of a polynomial, in order to reveal and exploit the structure of algebraic systems. This talk surveys compact formulae, including older and recent results, in sparse elimination. We start with root bounds and juxtapose two...

We rely on aggregate separation bounds for univariate polynomials to introduce novel worst-case separation bounds for the isolated roots of zero-dimensional, positive-dimensional, and overde- termined polynomial systems. We exploit the structure of the given system, as well as bounds on the height of the sparse (or toric) resultant, by means of...

This paper presents the average-case bit complexity of subdivision-based univariate solvers, namely those named after Sturm, Descartes, and Bernstein. By real solving we mean real root isolation. We prove bounds of $\sOB(N^5)$ for all methods, where $N$ bounds the polynomial degree and the coefficient bitsize, whereas their worst-case...

This paper implements algebraic elimination methods for an accurate and general calibration of parallel robots, applied to Gough (or Stewart) platforms. It focuses on two approaches, namely algebraic variable elimination and monomial lineariza- tion, which are compared to a classical numerical optimization technique. We detail the former, since...