In this paper, a new class of a weighted quadrature rule is represented as --------------------------------------------  where  is a weight function,  are interpolation nodes,  are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as   that  and we obtain the explicit expressions of the coefficients  using the q-...

A locally modular (resp. locally distributive) lattice is a lattice with a congruence relation and each of whose equivalence class has sufficiently many elements and is a modular (resp. distributive) sublattice. Both the lattice of all closed subspaces of a locally convex space and the lattice of projections of a locally finite von Neumann algebra are locally modular. The lattice of all /^-topo...

This paper presents a new approach for the Radial Basis Function (RBF) interpolation of a vector field. Standard approaches for interpolation randomly select points for interpolation. Our approach uses the knowledge of vector field topology and selects points for interpolation according to the critical points location. We presents the results of interpolation errors on a vector field generated ...

Rainfall data is useful in many fields such as urban management, agriculture, and so on. Spatial interpolation is widely used to interpolation continue rainfall data from discrete rainfall gauges. The uncertainty in spatial interpolation is change in different region. Paper focus on urban small area of Beijing city, Xicheng District and analyses uncertainty of spatial interpolation from four as...

In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point (so-called Gimbal Lock). However, quaternion interpolation has the advantage of natural (specifically smooth) orientation interpolation without Gimbal Lock. This paper presents the application of quaternion interpolation, specifically Spherical Linear IntER...

A novel interpolation algorithm, fuzzy interpolation, is presented and compared with other popular interpolation methods widely implemented in industrial and manufacturing applications. Different interpolation algorithms have been developed, reported and implemented in many industrial applications in recent years. Most of them are based on looking for the optimal interpolation trajectories base...

Many interpolation methods have been developed for high visual quality, but fail for inability to preserve image structures. Edges carry heavy structural information for detection, determination and classification. Edge-adaptive interpolation approaches become a center of focus. In this paper, performance of four edge-directed interpolation methods comparing with two traditional methods is eval...

One of the main challenges in software verification is efficient and precise analysis of programs with procedures and loops. Interpolation methods remain among the most promising techniques for such verification. To accommodate the demands of various programming language features, over the past years several extended forms of interpolation have been introduced. We give a precise ontology of suc...

Abstract. We consider the finite element approximation of the Laplacian operator with the homogeneous Dirichlet boundary condition, and study the corresponding Lagrange interpolation in the context of finite element superconvergence. For ddimensional Qk-type elements with d ≥ 1 and k ≥ 1, we prove that the interpolation points must be the Lobatto points if the Lagrange interpolation and the fin...

Linear interpolation requires a single multiplication but is signiicantly less accurate than quadratic interpolation. The latter requires two multiplications. Two novel quadratic interpolation schemes are shown here that approximate the functions required by the Logarithmic Number System (LNS) with more accuracy than linear interpolation using only a single multiplication. One method uses two R...