The theme of the present paper is numerical integration $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First initial interval partitioned into subintervals and integrand approximated by a piecewise polynomial interpolant based on obtained partition. Then approximation applied difference its interpolant. final integral sum both. optima...

Abstract We present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given simplicial mesh, we first refine the mesh into smaller simplices which can be used define forms. Cochains this refined then interpolated using Hence, when is with calculus, solution expressed as form. algorithms for three required steps: refining solving c...

In this paper I describe the implementation of a probabilistic regression model in BUGS. BUGS is a program that carries out Bayesian inference on statistical problems using a simulation technique known as Gibbs sampling. It is possible to implement surprisingly complex regression models in this environment. I demonstrate the simultaneous inference of an interpolant and an input-dependent noise ...

Mundici considered the question of whether the interpolant of two propositional formulas of the form F → G can always have a short circuit description, and showed that if this is the case then every problem in NP ∩ co-NP would have polynomial size circuits. In this note we observe further consequences of the interpolant having short circuit descriptions, namely that UP ⊆ P/poly, and that every ...

In this paper, a new set of spline functions called ``Flat End Fuzzy Spline" is defined to interpolate given fuzzy data. Some important theorems on these splines together with their existence and uniqueness properties are discussed. Then numerical examples are presented to illustrate the differences between of using our spline and other interpolations that have been studied before.

In this note a local thinning of the data locations is proposed, in order to construct a least squares multiquadric approximant stable and close to the multiquadric interpolant

We show that in dimensions four and higher, to insure a smooth interpolant, additional geometric constraints must be imposed on the generalized Clough–Tocher split introduced in Worsey and Farin (Constr. Approx. 3:99–110, 1987).

Craig interpolation is a well known method of abstraction successfully used in both hardware and software model checking. The logical strength of interpolants can affect the quality of approximations and consequently the performance of the model checkers. Recently, it was observed that for the same resolution proof a complete lattice of interpolants ordered by strength can be derived. Most stat...

Interpolation is an important technique in computer aided verification and static analysis of programs. In particular, interpolants extracted from so-called local proofs are used in invariant generation and bounded model checking. An interpolant extracted from such a proof is a boolean combination of formulas occurring in the proof. In this talk we first describe a technique of generating and o...

1 Background and Introduction Let 27 and H be two inconsistent first order theories. Then by Craig's Interpolation Theorem, there is a sentence 8, called a Craig interpolant, such that 8 is t rue in 27 and false in H and every nonlogical symbol occurring in 8 occurs in bo th 27 and H. Craig interpolants can be used to solve the problem of learning a first order concept by letting 27 and H be th...