Polynomials with quaternionic coefficients located on only one side of the powers (we call them simple polynomials) may have two different types of zeros: isolated and spherical ze...
Abstract. Minimizing the evaluation cost of a polynomial expression is a fundamental problem in computer science. We propose tools that, for a polynomial P given as the sum of its ...
Charles E. Leiserson, Liyun Li, Marc Moreno Maza, ...
We present exact and complete algorithms based on precomputed Sturm-Habicht sequences, discriminants and invariants, that classify, isolate with rational points and compare the re...
Abstract. We present three algorithms to calculate Φn(z), the nth cyclotomic polynomial. The first algorithm calculates Φn(z) by a series of polynomial divisions, which we perfo...
In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities ("Greeks"). These estimators are ba...