Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial interpretations very well known in the context of term rewrite systems (TRSs) to obtain new (non-transformational) termination analysis techniques for definite logic pro...

where ∗ denotes both the conjugate of a complex number and the conjugate of a matrix or an operator. The first result of this type is the well-known Fejer-Riesz theorem (Riesz and SzNagy, 1955), which states that if Π(iω) is a (scalar) polynomial, then we can choose a polynomial M(z) which, additionally, does not have zeros in the right half-plane. Extensions to polynomial, hence also to ration...

Let (pn)n be a given monic orthogonal polynomial sequence (OPS) and k a fixed positive integer number such that k ≥ 2. We discuss conditions under which this OPS originates from a polynomial mapping in the following sense: to find another monic OPS (qn)n and two polynomials πk and θm , with degrees k and m (resp.), with 0 ≤ m ≤ k − 1, such that pnk+m(x) = θm(x)qn(πk(x)) (n = 0, 1, 2, . . .). In...

In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation Linear Techniques, Blossoming and Groebner basis methods, our main focus is on algorithms defined by Polya’s theorem, Bernstein’s theorem and Handelman’s th...

We introduce a method for constructing a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show that this polynomial-based NLLS-optimized (PBNO) preconditioner significantly improves the performance of 2-D continuous Galerkin (CG) and discontinuous Galerkin (DG) compressible Euler equation models when run in an implicit-explicit time integration mode. When employed ...

It is well-known that the Legendre-Fenchel conjugate of a positive-definite quadratic form can be explicitly expressed as another positive-definite quadratic form, and that the conjugate of the sum of several positive-definite quadratic forms can be expressed via inf-convolution. However, the Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms is not clear at pres...

For each m 3 1, let A(m) = {N E Z x Z : Q(N) = m>. Note that CNEacrn) P(N) = 0 for each m > 1 if and only if e(,; P, Q) = 0. Let G denote the group of integral automorphs (of determinant &l) of Q(X). The first result in [I] states that if P(X) is a spherical polynomial with respect to Q(X) and if O(T; P, Q) E 0, then CUEG P(UX) = 0. The following theorem shows that this result holds for any hom...