Gauss-Seidel method is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for po...

This paper introduces a new technique for termination analysis of definite logic programs (LPs) based on polynomial interpretations. The principle of this technique is to map each function and predicate symbol to a polynomial over some subset of natural numbers, like it has been done in proving termination of term rewriting systems. Such polynomial interpretations can be seen as a direct genera...

Sums of convergent series for any desired number terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite terms the sum is obtained taking asymptotic limit polynomial. A function with second-degree polynomials both in numerator and denominator found to produce excellent results. different characteristics such as alternating signs co...

We consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the viewpoint of convex optimization. We relate the question to sums of squares decompositions of a certain Hermite matrix. If some power of a polynomial admits a de...

We describe an alternative construction of an existing canonical representation for definite Horn theories, the Guigues-Duquenne basis (or GD basis), which minimizes a natural notion of implicational size. We extend the canonical representation to general Horn, by providing a reduction from definite to general Horn CNF. We show how this representation relates to two topics in query learning the...

Discrete geometry and computational geometry are areas of active research that belong together, can benefit from intensified interaction, and need a common platform: This was the vision of Eli Goodman and Ricky Pollack in the mid-1980s, which led to the birth of Discrete & Computational Geometry. The journal they created in 1986 has documented, highlighted, and triggered many important breakthr...

We present LHIP, a system for incremental grammar development using an extended DCG formalism. The system uses a robust island-based parsing method controlled by user-defined performance thresholds.

When τ is a quasi-definite moment functional onP , the vector space of all real polynomials, we consider a symmetric bilinear form φ(·, ·) on P ×P defined by φ(p, q) = λp(a)q(a)+ μp(b)q(b)+ 〈τ, p′q ′〉, where λ,μ, a, and b are real numbers. We first find a necessary and sufficient condition for φ(·, ·) to be quasi-definite. When τ is a semi-classical moment functional, we discuss algebraic prope...

in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...