Interpolating provers have a variety of applications in verification, including invariant generation and abstraction refinement. Here, we extended these methods to produce universally quantified interpolants and invariants, allowing the verification of programs manipulating arrays and heap data structures. We show how a paramodulation-based saturation prover, such as SPASS, can be modified in a...

Forest cover requires large scale and frequent monitoring as an indicator of biodiversity progress towards United Nations World Bank Sustainable Development Goal 15. Measuring change in forest over time is essential task order to track preserve quality habitats for species around the world. Due prohibitive expense impracticality mass field data collection monitor at regular intervals, satellite...

The phenomena customly called Dark Matter or Modified Newtonian Dynamics (MOND) have been argued by Bekenstein (2004) to be the consequences of a covariant scalar field, controlled by a free function (related to the MOND interpolating function μ̃(g/a0)) in its Lagrangian density. In the context of this relativistic MOND theory (TeVeS), we examine critically the interpolating function in the tran...

We generalize the transfinite triangular interpolant of (Nielson, 1987) in order to generate visually smooth (not necessarily polynomial) local interpolating quasi-optimal triangular spline surfaces. Given as input a triangular mesh stored in a half-edge data structure, at first we produce a local interpolating network of curves by optimizing quadratic energy functionals described along the arc...

We describe an approximating scheme based on cubic C1 splines on type-6 tetrahedral partitions using data on volumetric grids. The quasi-interpolating piecewise polynomials are directly determined by setting their Bernstein–Bézier coefficients to appropriate combinations of the data values. Hence, each polynomial piece of the approximating spline is immediately available from local portions of ...

A corrected interpolating polynomial is derived. Error inequalities of Ostrowski type for the corrected interpolating polynomial are established. Some similar inequalities are also obtained.

In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exactly interpolating methods are often proposed for the exact results and approximate interpolating methods for the approximate...

the current paper proposes a technique for the numerical solution of linear control systems.the method is based on galerkin method, which uses the interpolating scaling functions. fora highly accurate connection between functions and their derivatives, an operational matrix forthe derivatives is established to reduce the problem to a set of algebraic equations. several testproblems are given, a...

A generalized recursive interpolation technique for a set of linear functionals over a set of general univariate basis functions has been previously developed. This paper extends these results to restricted multivariate interpolation over a set of general multivariate basis functions. When the data array is a suitable configuration (e.g., an ^-dimensional simplex), minimal degree multivariate i...

In this paper odd-order B-spline filters are proposed to reconstruct volumetric data sampled on an optimal Body-Centered Cubic (BCC) grid. To make these filters nearly interpolating, we adapt a previously published framework, which is based on a discrete frequency-domain prefiltering. It is shown that a BCC-sampled B-spline kernel is not invertible, therefore the interpolation constraint cannot...