Displaying similar documents to “Multivariate Sturm-Habicht sequences: real root counting on n-rectangles and triangles.”

Finding the roots of polynomial equations: an algorithm with linear command.

Bernard Beauzamy (2000)

Revista Matemática Complutense

Similarity:

We show how an old principle, due to Walsh (1922), can be used in order to construct an algorithm which finds the roots of polynomials with complex coefficients. This algorithm uses a linear command. From the very first step, the zero is located inside a disk, so several zeros can be searched at the same time.

On stable polynomials

Miloslav Nekvinda (1989)

Aplikace matematiky

Similarity:

The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.

On a Theorem by Van Vleck Regarding Sturm Sequences

Akritas, Alkiviadis, Malaschonok, Gennadi, Vigklas, Panagiotis (2013)

Serdica Journal of Computing

Similarity:

In 1900 E. B. Van Vleck proposed a very efficient method to compute the Sturm sequence of a polynomial p (x) ∈ Z[x] by triangularizing one of Sylvester’s matrices of p (x) and its derivative p′(x). That method works fine only for the case of complete sequences provided no pivots take place. In 1917, A. J. Pell and R. L. Gordon pointed out this “weakness” in Van Vleck’s theorem, rectified it but did not extend his method, so that it also works in the cases of: (a) complete Sturm sequences...