It is well known that solving polynomial equations, or finding the eigenvalues of matrix polynomials, can be done by transforming to a generalized eigenvalue problem (see for example [10]). In this paper we examine a new way to do this directly from the values of the polynomial or matrix polynomial at distinct evaluation points.

We compare the complexities of multipoint polynomial evaluation and interpolation. We show that, over a field of characteristic zero, both questions have equivalent complexities, up to a constant number of polynomial multiplications.

We define a multivariate polynomial that generalizes several interlace polynomials defined by Arratia, Bollobas and Sorkin on the one hand, and Aigner and van der Holst on the other. We follow the route traced by Sokal, who defined a multivariate generalization of Tutte’s polynomial. We also show that bounded portions of our interlace polynomial can be evaluated in polynomial time for graphs of...

In this paper, we consider an algorithm that efficiently evaluates a trigonometric polynomial at arbitrarily spaced nodes. It is based on the approximation of the polynomial by a function we can evaluate easily. We are particularly interested in the case where we interpolate the trigonometric polynomial using high-order cardinal interpolation kernels known as Z-splines, which we construct and s...

It is shown that the compressed word problem of a graph product of finitely generated groups is polynomial time Turing-reducible to the compressed word problems of the vertex groups. A direct corollary of this result is that the word problem for the automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Moreover, it is shown that a res...