The current implementation of Thiele rational interpolation in Maple (the Thieleinterpolation routine) breaks down when the points are not well-ordered. In this article, it is shown how breakdown can be avoided by ordering an adaptive way.

As a kernel independent algorithm, multilevel Green’s function interpolation method (MLGFIM) [1] [2] has been developed for electromagnetic problems from low frequency to fullwave simulation. This method inherits the multilevel tree structure of multilevel fast multipole algorithm (MLFMA) and adopts the interpolation technique of pre-corrected fast Fourier transform (PFFT). Compare with other f...

In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this topic. We also explore the relation between classical interpolation and sparse interpolation. We second consider the design of the interpolation points for th...

Models of contour interpolation have been proposed for illusory contour interpolation but seldom for interpolation of occluded contours. The identity hypothesis (Kellman & Loukides, 1987; Kellman & Shipley, 1991) posits that an early interpolation mechanism is shared by interpolated contours that are ultimately perceived as either illusory or occluded. Here we propose a model of such a unified ...

We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago. We also discuss computational differences and give examples of other cubic interpolation schemes not pre...

Divide-and-conquer method for interpolation in Guruswami-Sudan (GS) list decoding algorithm is considered. It is shown that the Groebner basis (GB) of the ideal of bivariate interpolation polynomials (IP) can be obtained as a product of trivariate polynomials corresponding to disjoint subsets of interpolation points. The impact of monomial ordering on the interpolation complexity is studied.

The problem of the linear interpolationof nonstationarymultidimensional processes with stationary increments is studied. The expressions of the interpolation filters and of the estimation error are derived, which generalize the results of the interpolation theory for stationary processes. Both finite and infinite extent interpolation are considered. An application to the interpolation of an und...

We consider the problem of image interpolation from an adaptive optimal recovery point of view. Many different standard interpolation approaches may be viewed through the prism of optimal recovery. In this paper we review some standard image interpolation methods and how they relate to optimal recovery as well as introduce a broader, more general and systematic approach to image interpolation u...

Fuzzy rule interpolation is an important technique for performing inferences with sparse rule bases. Even when given observations have no overlap with the antecedent values of any rule, fuzzy rule interpolation may still derive a conclusion. Nevertheless, fuzzy rule interpolation can only handle fuzziness but not roughness. Rough set theory is a useful tool to deal with incomplete knowledge, wh...

A key problem in environmental monitoring is the spatial interpolation. The main current approach in spatial interpolation is geostatistical. Geostatistics is neither the only nor the best spatial interpolation method. Actually there is no “best” method, universally valid. Choosing a particular method implies to make assumptions. The understanding of initial assumption, of the methods used, and...