A note on zeros of univariate scalar Bernstein polynomials

In Machchhar and Elber (2016), an algorithm is presented for computing all real roots of univariate scalar Bernstein polynomials by subdividing the polynomial at a known root and then factoring out the root from the polynomial, resulting in a reduction in problem complexity. This short report presents a speed-up over Machchhar and Elber (2016), by circumventing the need for subdividing the polynomial each time a root is discovered, an O(n²) process, where n is the order of the polynomial. The subdivision step is substituted for by a polynomial division. This alternative also has some drawbacks which are discussed as well.