A note on imputing squares via polynomial combination approach

relaxed stabilization conditions via sum of squares approach for the nonlinear polynomial model

in this paper, stabilization conditions and controller design for a class of nonlinear systems are proposed. the proposed method is based on the nonlinear feedback, quadratic lyapunov function and heuristic slack matrices definition. these slack matrices in null products are derived using the properties of the system dynamics. based on the lyapunov stability theorem and sum of squares (sos) dec...

Note on a polynomial of

Computing f(A)b via Least Squares Polynomial Approximations

Given a certain function f , various methods have been proposed in the past for addressing the important problem of computing the matrix-vector product f(A)b without explicitly computing the matrix f(A). Such methods were typically developed for a specific function f , a common case being that of the exponential. This paper discusses a procedure based on least squares polynomials that can, in p...

A Note on Property Testing Sum of Squares and Multivariate Polynomial Interpolation

In this paper, we investigate property testing whether or not a degree d multivariate polynomial is a sum of squares or is far from a sum of squares. We show that if we require that the property tester always accepts YES instances and uses random samples, nΩ(d) samples are required, which is not much fewer than it would take to completely determine the polynomial. To prove this lower bound, we ...

On Squares in Polynomial Products

Let f(X) ∈ Z[X] be an irreducible polynomial of degree D ≥ 2 and let N be a sufficiently large positive integer. We estimate the number of positive integers n ≤ N such that the product F (n) = n ∏