A traditional interpolation model is characterized by the choice of reg-ularizer applied to the interpolant, and the choice of noise model. Typically , the regularizer has a single regularization constant , and the noise model has a single parameter. The ratio == alone is responsible for determining globally all these attributes of the interpolant: its`complexity', ``exibility', `smoothness', `...

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid.The rational interpolant is of the formmotivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are bas...

In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using derivatives are presented. The combination tension, continuity, bias control is used as a very powerful type interpolation; they applied to curves. Surface construction utilizing studied explored several examples obtained by C1 surface given show usefulness method.

We provide an overview of spline and wavelet techniques with an emphasis on applications in pattern recognition. The presentation is divided in three parts. In the first one, we argue that the spline representation is ideally suited for all processing tasks that require a continuous model of the underlying signals or images. We show that most forms of spline fitting (interpolation, least-square...

Logical interpolants have found a wide array of applications in automated verification, including symbolic model checking and predicate abstraction. It is often critical to these applications that reported interpolants exhibit desired properties, correctness being first and foremost. In this paper, we introduce a method in which interpolants are computed by type inference within the trusted cor...

We solve the problem of C2 Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of C2 space boundary data (two points with associated first and second derivatives) we construct a four–dimensional family of PH interpolants of degree 9 and introduce a geometrically invariant parameterization of this family. This parameterization is used to identify a parti...

We show methods to extract Craig-Lyndon interpolants and access interpolants from clausal first-order tableaux as produced by automated first-order theorem provers based on model elimination, the connection method, the hyper tableau calculus and instance-based methods in general. Smullyan introduced an elegant method for interpolant extraction from “non-clausal” first-order tableaux. We transfe...

introduction 3d reconstruction of an object from its 2d cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. in order to perform 3d reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. mate...

In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarević operators. By exhibiting a generalized “taxi-cab” metric, we show that the graph of a bilinear fractal interpolant is the attractor of an underlying contractive bilinear IFS. We present an explicit formula for the box-counting dimension of the ...