4. Hermite Interpolants . . , . . . . . . . . . . . . . 104 4.1. The Co nine parameter interpolant ...... 104 4.2. C’ quintic interpolants .............. 104 4.3. The general case ................... 106 5. Split Triangle Interpolants . . . . . . . . . 107 5.1. The C’ Clough-Tocher interpolant . . _ . . 108 5.2. Limitations of the Clough-Tocher split . 110 5.3. The C’ Powell-Sabin interpolants ...

orthogonal zero interpolants (ozi) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. ozi’s can be constructed by the 3-term recurrence relation. these interpolants are found useful in the solution of constrained approximation problems and in the structure of gauss-type quadrature rules. we present some theoretical...

Spline quasi-interpolants are local approximating operators for functions or discrete data. We consider the construction of discrete and integral spline quasi-interpolants on uniform partitions of the real line having small infinite norms. We call them near minimally normed quasi-interpolants: they are exact on polynomial spaces and minimize a simple upper bound of their infinite norms. We give...

Propositional interpolation is widely used as a means of overapproximation to achieve efficient SAT-based symbolic model checking. Different verification applications exploit interpolants for different purposes; it is unlikely that a single interpolation procedure could provide interpolants fit for all cases. This paper describes the PeRIPLO framework, an interpolating SAT-solver that implement...

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...

One of the main challenges in software verification is efficient and precise compositional analysis of programs with procedures and loops. Interpolation methods remains one of the most promising techniques for such verification, and are closely related to solving Horn clause constraints. We introduce a new notion of interpolation, disjunctive interpolation, which solves a more general class of ...

We present a method to compute uniform interpolants of ALC-ontologies with ABoxes. Uniform interpolants are restricted views of ontologies that only use a specified set of symbols, but share all entailments in that signature with the original ontology. This way, it allows to select or remove information from an ontology based on a signature, which has applications in privacy, ontology analysis ...

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model checking, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, litt...

Orthogonal zero interpolants (OZI) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. OZI’s can be constructed by the 3-term recurrence relation. These interpolants are found useful in the solution of constrained approximation problems and in the structure of Gauss-type quadrature rules. We present some theoretical...